Eh, that swinginess also exists in attack rolls and other ability checks, so I don't mind it that much. Thing is, it shows that there are only 4 initiative positions, since everyone ends up being grouped together one way or another. I'd much have preferred the swinginess to basically being guaranteed that everyone will be grouped together.
Not to the same degree. It's not even arguable. It's simple math. With attacks and skills and so on you get proficiency, stat, magic items and a bunch of other bonuses like bless, guidance and so on.
With initiative you get DEX.
That's it, apart from one feat and very rare class features, which, unless you also have high DEX, are basically meaningless because of the RNG. There's a whole extra level of stupidity in that they made it DEX only rather than INT or DEX, presumably solely out of spite towards 4E, which helps make 5E's INT-dumping problem worse.
It's straight up bad design that does not fit well into 5E's design paradigm and makes the game worse on every level - less tactical, less thoughtful, more ludicrous, less possible to influence by good decisions in game or character/class abilities, and so on. It's absolutely one of the worst aspects of 5E and was clearly half-assed, like Hit Dice, another mechanic this game sensibly throws overboard.
Like I said, d4 is going too far but d20 is junk design the way 5E has done it.
5E is also terrible at surprise rounds and the concept of surprise generally. It might be the worst edition of D&D for it.