If something is a must-have for every participant (with a very miniscule number of exceptions)... is that healthy for a game? What are some possible reworks to make Flash have a better niche than just "Take it or lose"?
You are asking the wrong question. Why is it NOT healthy? Just cause its usually must have is not a valid answer.
Look at it this was. You can use it to make slick engages, or frantic escapes. Can secure kills, objectives, make sick plays.
What is negative about any of that?
You can pretend its bad, but imagine if it was gone. Things would feel a lot more bland. Half the champ pool would always die if they got ganked, if you had no mobility you couldn't escape.
Lanes would get stale as people would be less likely to push lanes in many scenarios.
There just is no negative to flash, and its fun to have in the game
Without it low mobility champions would not be viable at all, unless they're super tanky or have good CC
Make immobile champions have more power.
That's literally the biggest reason it cannot be removed ever. If Flash was removed, immobile champions would, for the most part, become irrelevant thanks to mobility.
Because taking something other than flash becomes an important strategic tradeoff, and the existence of flash allows for champions who can commit heavy resources every 5 minutes into a play (like annie flash ult) without being able to do it every team fight.
Like I said, I think the only solution is to make Flash it's own special category. Like an innate feature for all champions (kinda like Recall I guess?). That way we have an extra Summ Spell slot freed up for other potential builds.
Tricky question,How do you think 
is healthy for the game?
Every champion whose kit has a dash can no longer bring flash. Boom. It's balanced and niche.
You're askign a question that's been brought up time and again throughout League's history. And yet the only remedy was to give it a longer cooldown. But then that began to wear down to the point where "any longer and it would become unviable and yet still wouldn't solve the problem."
What they should really do to remedy the situation, since it's so vital to pretty much every aspect of the game, is just make it an innate ability that doesn't take up a whole Summoner Spell slot. Maybe it could even be something tied to the Boots items (since everyone gets boots)?
The problem is that it's far too late to really do much to it without completely warping the game. At this point they need to add a couple more summoners and tweak the ones we have so I have a reason to actually look at replacing it.
Because we don't want Tibbers to have 1,000 range every 60 seconds. ;)
Someone earlier mentioned if any champ with a dash couldn't use Flash. Effects? Issues? Benefits?
How would things be different if perhaps players were only offered once Summoner? Thus giving you a choice between say, TP or Flash..
It's not a take it or lose it. But it is great just in case you stop paying attention and get into some deep shit... you can just flash out :D
STFU
