I think it can be a big deal, and flying PC's probably shouldn't be hard-coded into every game, but I also think that it can NOT be a big deal, and flying PC's should not be disallowed from Level 1. Treating them as opt-in makes a lot of sense for me.
All I can really do here is agree to disagree. Personally, I feel that flight is something which is a big deal. Are there ways a game can make it not a big deal? Probably, but most of the methods I've seen from D&D (4E in particular) tend to involve methods which bother me for other reasons.
Yeah, but that's only a problem if you use a battle mat.
Or care about the positions of battlefield pieces in relation to each other.
You can also do this if you're a teleporting blink-elf. Or a sneaky rogue. Or a barbarian who goes SMASH and knocks everything aside. Or if you have a bow.
I can only assume you mean Eladrin here. If that's the case, it's important to point out that Eladrin cannot teleport at-will. So, while there is some thematic overlap in so much that 4E Eladrin also have an option which increases their ability to move, that option is limited. The sneaky rogue and smash-happy barbarian both are still opposed by the enemy.
I'm not quite sure what a bow has to do with it -unless you're assuming a ruleset which allows you to shoot through the enemy. I'll be honest, my knowledge of 4E rules has atrophied quite a bit, but I believe you could not shoot through the enemy to hit foes which you could not see. In other iterations of D&D (as well as other rpgs) your allies get in the way as well. That being said, a flying combatant with a bow most certainly could fly to a higher altitude for the purpose of being able to hit a specific target without needing to worry about obstacles in between.
Well, catching yourself in a spell by accident was antiquated right around 2e.
I don't think that's much of a concern.
Some 4E Burst and Blasts targeted anyone inside the area of effect. Having an ally who is capable of doing battle with the enemy will also being above the area of a harmful effect is an advantage. In other versions of D&D (and other rpgs) there are other considerations as well.
Not following you...a dude with a bow in 4e can target pretty much anything on the battlefield. Flying doesn't change that.
Again, I'll admit to my knowledge of 4E suffering from atrophy, but I'm of the belief you cannot shoot through enemies to hit enemies who are behind them. Also, not all versions of D&D follow the same rules as 4E; some gave penalties for firing through your allies, into melee; as well as a variety of other modifiers.
Cleric can also teleport, or smash, or jump, or....
At-will and at level 1?
I'll give you the jumping though; especially if we're looking at 4E. Jumping over foes was a tactic I used a lot; it wasn't hard to get a good enough athletics check to bound over foes. I'll again also say that a cheesy (but effective) 4E tactic was to jump before using a Burst or Blast so as to hit a bigger area.
And accidentally healing enemies isn't something D&D has ever had much of...
See some of my comments concerning burst and blasts above, but read being able to hit the enemy without hitting an ally as being able to heal and ally without hitting the the enemy instead.
Only if there's no wind, clouds, updrafts, downdrafts, cliffs....not to mention the strength and stamina needed for long-duration flight.
Flying has its own environmental challenges.
While I agree such things should be a factor, and I also agree that turning radius and maneuverability (as mentioned by Hussar and Klaus) should be concerns, such things often are not when playing D&D. I would be supportive of a system in which they are, and that would make me more inclined to view flight as possibly more balanced against other advantages, but I'm admittedly skeptical that baseline 5th Edition would handle 1st level flight in a way I'd find balanced against some of the other options. That's not say D&D never handles flight well; the 4E Pixie came across better than I expected, but -in general- I've found the implementation to be somewhat poor. 3rd Edition has a plethora of rules for handling flight and maneuverability, but they tend to be somewhat clunky, and it's a rare group that I've played with that pays any attention to them -though I can hardly fault the game for a group playing a game while ignoring some of the rules. My experience with 1st and 2nd edition isn't enough for me to have a knowledgeable opinion.