The movement inhibitors would shut down a lot of reactive movement abilities, and some feats and abilities trigger off of status effects: Net Snare, Iron Soul Flurry of Blows, etc.
In a one on one fight, Net Snare is mostly useless as written. It should be until end of your next turn. Even in a party, burning off a standard action to grab a foe is generally considered a waste of an action. Doing so and it auto-ends at the start of your next turn is just plain lame. This is a terrible power that could use a boost of until end of your next turn. Bad example.
Iron Soul Flurry of Blows? Another bad example. Foes cannot shift on your turn (shy of them or one of their allies using an interrupt to do so), so it doesn't matter if it ends at the start or end of your next turn. The odds of an enemy having such an ability and using it are probably one in a thousand.
Your examples here have no teeth to them and this is why I asked for examples. It's one thing to make the claim, it's another to back it up with examples that really illustrate the claim.
Aura and zone abilities could be more easily abused in conjunction with movement powers, and you could even have TWO of them up at the same time in the right circumstances: Ignition, Rotting Doom, Body Double, etc.
I can see where at first glance you might think this with Ignition. However, Ignition is not enemy only. It's any creature. So if you think about it, the extra damage from the Ignition zone is a two edged sword. NPCs can take it. PCs can take it. Because of this, it does force NPCs initially caught in it to leave it or take a very small amount of damage. But, does it really matter if the Sorcerer can slide some NPCs back into it for CON damage each on the following turn? Sorcerers have very few forced movement powers and most of them are one square, most of them are single target (Beguiling Burst is a once per encounter exception), and most of them are Dailies. Yes, a small synergy can be set up here, but compared to many other synergies in the game system, this is small potatoes.
Rotting Doom? Not seeing it. Foes very rarely heal in the first place. How many foes can heal themselves or possibly an ally on your turn with an immediate interrupt? This is another bad example.
I'll concede Body Double with a caveat. Think about it for a second. A first level PC can be in two places at once and can do so At Will. In earlier editions of the game, that would have been something like a 5th level or higher spell. So yes, they had to put limitations into Body Double, otherwise, it would have really been an overpowered power. But, two places at once? At first level? And At Will? Come on WotC. Just because someone can think of an idea doesn't make it a good one. As an At Will power (which it should have never been), end of next turn is too potent for Body Double. If Body Double was an Encounter power instead of an At Will, then end of next turn would be totally fine for it since the main extra gain is the bonus combat advantage for flank the following round.
So, I'll concede it for this power, but I personally think that this power is way too uber for level one as an At Will and should have never seen the light of day in the game. One poorly conceived power does not really illustrate your point. When one compares the ability to defend a 15 square area compared to the 9 square area of other defenders as a first level At Will plus it increases the number of potential flank squares on the board from 8 to 17 for the Defender, this power is just plain wrong compared to virtually every other defender first level At Will power in the game. So yes, it's already too potent (utility-wise) as a first level At Will and making it more potent with end of turn would be a mistake.
Special combos can crop up where you can use one ability to magnify another: Karmic Bond+Unconscious Assault, Paint the Bulls-Eye+Direct the Strike, etc.
Karmic Bond + Unconscious Assault? Are you serious? Ok, this is a little complex here, but the gain here is almost non-existent.
Let's compare current version vs. modified version:
Current:
Round one: Ardent hits foe with Karmic Bond. Foe hits someone else. A PC ally hits and the foe takes CON damage.
Round two: If all PC allies missed, then the Ardent can do the extra CON damage with any attack. The power already lasts until the end of the next turn, it's just the enemy attack that must occur before the start of the next turn.
Modified:
Round one: Ardent hits foe with Karmic Bond. Foe hits someone else. A PC ally hits and the foe takes CON damage.
Round two: If all PC allies missed, then the Ardent can do the extra CON damage.
or the only time it would matter:
Round one: Ardent hits foe with Karmic Bond. Foe
misses someone else.
Round two: Ardent can do Unconscious Assault and the foe can attack and possibly hit a different foe.
Here's the problem. The Ardent used up his Standard Action already in the second round when the foe missed on its turn. The Ardent doesn't have a standard action left over to attack that foe again, hence, this gains ZERO. Yes, he could use an Action Point, so he could possibly do extra CON damage once every other encounter with this trick. At 27th level, there's a lot better tricks than this. Even the augment 2 version of Karmic Bond doesn't do much here. This is white noise and a terrible example for your POV.
Paint the Bulls-Eye + Direct the Strike. This is potentially a legitimate example, but again, think about it. As written, Paint the Bulls-Eye in a 5 PC team allows upwards of 4 * Int or Wis extra damage already. This would up it to 5 * Int or Wis extra damage if changed to end of next turn combined with Direct the Strike. So yes, it would allow for upwards of 2 to 4 extra points of damage every other round at low level. But, it is already allowing upwards of 8 to 16 extra points of damage every other round in a 5 PC team. Is a potential 2 to 4 more every other round really that potent? Not really. Nice? Definitely. Broken? Not even close. At first level, this would drop a 6 round encounter to a 5.7 round encounter (1 to 2 extra points per damage per round * 75% chance to hit vs. 5 30 hit points foes at first level). Measurable, but not overly potent considering that Paint the Bulls-Eye used with or without Direct the Strike is already a striker level power/combo that can easily drop an encounter by 1.5 rounds over the vast majority of other non-striker At Will powers in the game system.
This is a solid extra synergy, but it's not game breaking.
Abilities that start creating a stacking loop that amplifies the effect: Memory Hole/Eyebite, Playful Torment, Brash Strike, etc.
Course, Memory Hole already has an augment 1 that does this, so meh.
I've always consider powers like Playful Torment to be a waste of space. Oh boy! You allow me to get a bonus to hit AFTER I already hit. Sorry, but these powers do not need to be in the game system. Except for once in a blue moon Action Points combined with a Daily and a once in a blue moon Opportunity Attack, gaining +2 to hit after the attack has already occurred is useless. Changing this to end of turn would actually make it worth taking. This is wasting your At Will power, just for a rare opportunity to set up a Daily once ever other encounter.
Brash Strike is another terrible example for you. Giving your foe Combat Advantage until start or end of your next turn is only going to matter if the foe can OA or Interrupt the fighter's attack on his turn. That would be super rare.
And please note, that's JUST At-Will powers. The combos you can do with Encounter and Daily powers can get nuts.
Yeah, I'm not going to debate this with you more. Your At Will examples were not that convincing and several of them are just plain awful for illustrating your POV.
Yes, there are some small synergies that can occur, but that doesn't mean that taking 4E powers over to 5E means that they have to be written exactly as is in 5E.
If there are a few powers here and there that could gain a really significant synergy, the designers can re-write those powers.
The point is, nothing you've written here shouts STOP THE PRESSES. A duration of until the start of your next turn is needed. Your examples merely show that at best, a few powers might need to be slightly re-written or tweaked and at worse (like with Playful Torment), the power actually becomes worthwhile more than once every other encounter if it is changed to end of turn.