Tracking saving throw times and concentration is too difficult.
Concentration is a part of nearly half of all spells.
For example, would a Paladin really bother with Shield of Faith
giving AC+2 if he just loses that spell when casting Bless which
also requires concentration?
Because they are for two different situations. Shield is good if the Paladin is trying to hold the line and draw attacks, bless is for the paladin helping himself and allies do lots of damage.
Why do the gaming mechanics use minutes at all?
Why not just say concentration for 10/10 turns?
Or concentration for encounter duration?
Because for many spells this would a ridiculous number to put down. Reading 1 hour duration is much easier to parse than 600 turns. Many spells that last longer than 1 minute can be used in multiple combats depending on situation, and there is some amount of out of combat travel. I would rather approximate it than track it in initiative.
Many maneuvers such as Feint Attack and spell effects such as
Searing Smite and Hunter's Mark should start before the attack.
Why make the character wait until his next attack?
Seems like the designers are a bit confused with the wording on
much of this timing.
All of those can be used before attacking. You do not have to take an action before your bonus action. You can do bonus action then action. You can Move, Action, Move, Bonus Action, Move. There is no strict ordering.
Now on to saving throws.
It is very difficult to remember and players often forget when
to role a save.
What the game wants is to have the spell effect during the target's turn.
Have all the initial saves before the target takes damage.
Have all recurring saves at the end of the target's turns each round.
No more saves at the start of the target's or caster's turn, or at the end of the caster's
turn.
In general there at a lot of things to keep track of. as the DM I keep track of things for monsters, and if I have mental space left over I help the players. However, most of the time, I do monsters, the players do players. IFF we both forget, when we remember I have all the saves apply immediately and adjust the damage accordingly. This applies for monsters needed to concentrate, players concentrating, any saves on both ends.
As for when things trigger it follows a generally regular pattern. First and foremost spells with no duration you do the save once when the spell happens and that's it, ezpz. Spells that apply an effect are generally save, then save at the end of each turn. Unless concentration is broken they last for one round.
Concentration spells that do area damage trigger twice. Once when someone enters it for the first time in a turn, and second at the start of that characters turn. Rarely will it trigger on enter or end of turn. The only spell I can immediately think of that does this is Wall of Fire.
In summary,
Saving throw timing needs to be simplified.
The target saves before taking initial damage or getting a damage condition.
The target saves again at the end of each of the target's turns.
Spell and Martial Effect timing needs to be simplified.
The spell, feat, maneuver grants advantage or adds damage, etc. instantaneously.
Spells that cause damage should require concentration.
If the spell increases armor class or abjures in some way, it shouldn't require
concentration.
Some of those things are already true, you just need to review the rules in chapters 7-9 again. Lots of good stuff in there. I am mostly against buffs being non-concentration. Having DMed pathfinder the number of named NPCs with a list of buff spells cast before combat was absurd. Then the players started stacking them and I was unenthused. The concept of 1 player -> 1 buff makes tracking things simple. Especially combined with advantage/disadvantge. If I never have to say "Did you remember +2 from the bard singing" or, "Are these both shield bonuses?" I would be happy.
Except that despite all its flaws and pain it's really fun to do absurd fantasy things in an everything goes world. So I will continue to 5e and pathfinder.