Kabouter Games
Explorer
Every edition of D&D has been class-based.
In name only.

And you could advance in 2-3 classes simultaneously, in the classic game, not just 'switch careers.'
Only after a certain point. If you switched from, say, Fighter to Thief, you had to use the Thief tables for everything. If once you used your Fighter abilities, you lost the XP for the entire adventure. Until your Thief levels surpassed your Fighter levels; then you could use the abilities interchangeably. That's what I meant by changing careers.
The later systems removed that consequence, in my opinion for the worse.
Then maybe there's an issue with what the DM wants, or with the opinion that a good DM doesn't say 'No.'
I'm OK with the first-say-yes style, mostly, but in 5e, y'gotta say 'No,' (and a lotta other things, too), sometimes. Because you have too much of the power to cede a lot of it just to avoid an uncomfortable situation.
Essentially, saying 'no' without having to actually say it. Which is, well, I'll try to find a nice way to say it...
...nope, sorry can't find one.
I'll go with: Worse than just saying 'no.'
That was very poorly worded on my part. I'm not saying a good DM never says "No." I'm saying a good DM starts from a position of "Let's work on it and see what we come up with." Only after every reasonable method of accommodating the player's concept is exhausted should the DM say no.
That's why I have to take great issue with "worse than just saying no."
Of course there's...
Unavoidable, but all the more reason to have more official options so people aren't tempted to push the crazy stuff on you.
"Can I use the DMsG 'Oriental Abominations' Supreme Samurai Class, the one who can kill everything within six miles in one action with Supreme Cleave?"
"Er, no*, use the official Samurai class from Volo's Guide to Kara-Tur, instead, we're all-official at this table."
* yeah, had to say no, sorry.
...which is entirely reasonable.

Ciao,
Bob (who really has to stop posting on ENWorld and get back to work on the material he's going to throw at his players day after tomorrow. ;P )