What happens when they use teleport to get to a safe place
It's a 7th level spell. I doubt we will get to the level where it can be used (13) for years, and once we do, it will be the mage's one and only 7th level spell slot. No really a concern for me.
or throw up an illusionary wall to rest in a cul de sac
So you're in the military, and the enemy just entered your base, killed a bunch of your friends, and is now holding up to rest so they can kill the rest of you. And you what, just sit there?
No, you react to the threat.
If a wall just appeared out of nowhere in your house, you'd notice, and start poking at it right away, with all your friends preparing to attack.
And, I think that is usually a concentration spell, so they won't be resting if they do. In fact, I think ALL illusions that can create a wall are concentration...so not even possible given it's the mage who needs to rest the most.
We all know the DM can mitigate anything in D&D with the clever use of story telling, however it can ruin the story or even the play experience of the party.
Creatures reacting logically to things trying to destroy them does not ruin the story or the experience, it enhances it. You've yet to demonstrate anything that would be harmful to the story or experience.
For instance after clearing half a dungeon the party Strength character moves some rubble to block the corridor to the part of the dungeon they haven't explored. Then all of a sudden half way through their extended rest they interrupted by the same kinds of monsters in the dungeon. After taking them out and later clearing the rest of the dungeon they find out there are no other exits and they didn't find any fresh tracks going out. So it breaks their immersion in the game.
I don't do that, I've mentioned previously I think this is a mistaken interpretation of what wandering monsters are, and it's not a concern.
Throwing up a wall of stone in front of a door or using something like stone shape (not sure if its in 5E yet, but it will be) to create a safe resting place is common.
They players have just as much trouble getting out as something else has getting in. If they players can just break it down, so can a creature. Again, if a wall appeared in your house, wouldn't you react to it? Particularly if you think there is a known killer who wants you dead behind that wall?
So the DM will definitely have to deal with the 5 minute work day, and the only thing that really happens is the players get more clever and the DM has to get more unrealistic to stop them.
You've yet to show me anything unrealistic. You claim it, but you have not shown it. So far it's more realistic, which is a feature and not a bug. If you go into somethings lair, start killing intelligent creatures and then stop to rest, the remainder of the creatures there will react appropriately to gather together, send for help, flee, prepare an ambush, prepare traps, mass assault you, etc.. That's what intelligent creatures would logically do in response to such a threat that has suddenly paused in the midst of their lair.