Is there any info on why NRD was removed from Wild Sorcerers (compared to previous editions, since NRD was one of the reasons the class was well-liked)?
Nahal's Reckless Dweomer has been directly incorporated into the Sorcerer's class features.
Starting in 3.5E, the spell was converted into the "Reckless Dweomer" class feature for the Wild Mage prestige class:
5th Edition goes a step further and makes all of a Wild Magic Sorcerer's 1st-level and higher spells function this way.
There are a few good reasons for the changes.
As [a Is there some reason Wild Sorcerers don't have Nahal's Reckless Dweomer in 5E? states, Wild Surge is the 5th ed version of Nahal's Reckless Dweomer. But in fact, it works much more like the original feature (which I wasn't aware of until it was described here) than it may seem at first.
First--it's worth noting that in general, a solid GM is going to invoke Wild Surge any time they are allowed to if the player is playing a wild sorcerer -- unless either:
This is because in 5e, the results of Wild Surge are, while as usual mixed, overwhelmingly positive. So having surges go off with regularity is simply part of the character's class feature (it also means that the player can use the die roll manipulation feature (tides of Chaos) frequently, which they're supposed to unless they're trying to avoid random chaos).
This means that when run correctly, a 5e wild mage is going to act pretty similarly to what you've said about a 2e wild mage, except in some ways better (if more balanced):
Mind, there are absolutely 5th level spell effects on the default table -- a 5th level MM, the bonus action teleport for a minute, the polymorph effect (if you save, anyway), and the minute of life insurance via reincarnate.