The (unwritten) rule of internal setting consistency; in that without levels (or magic items) where does that power come from and how can it be explained?
I believe that the power comes from the world, not from levels. The fact that there are levels to explain power progression is a (not completely necessary, but useful) evil, but it does not mean that it has to be the same for everyone in the multiverse. Mindflayers don't have levels, lots of creatures can cast spell spontaneously. Some NPCs can have training just like PCs, but others might acquire things differently, through pacts or through any training that would be different from the PCs.
Indeed. Not all "classes" are adventuring-based*, and even those that are have stay-at-home equivalents. For example: a stay-at-home lab wizard will still acquire experience points and levels through doing what she does and learning in the process, albeit much more slowly than her field-adventuring counterpart. And I have "classes" that aren't field-adventuring based - artificer being the one most commonly encountered by PCs. If someone really wanted to play an artificer as PC I'd allow it, but the projected survival rate would be extremely low (they don't gain h.p. by level, for one thing) and very few of their abilities would be of any use in the field: the character would be a passenger.
* - 3e took this concept completely overboard with dumb things like the Commoner class, but the underlying idea has merit.
Not to everyone, it's again a totally artificial limitation.
I've had one or two bad DMs and luckily managed to avoid a few others by hearing the stories from trusted friends. I've also had some very good DMs, and for a much longer time.
And, honestly, where the DMs really bad or did they simply have a different playstyle, or were they just inexperienced ?
Refer above to the unwritten rule of internal setting consistency.
I prefer world consistency rather than rules consistency. The game (and in particular 5e) supports both, after that preferences depend only on your playstyle.
I'm not saying that I don't understand you, one of the advantages of 3e is that it should have been easier to compute relative power of creatures and therefore to balance encounters technically, unfortunately it did not work because powers were still not equal in particular when combined.
But as I'm not overly concerned about balance, I prefer being free to put powers where they well nice and will help NPCs look badass and provide a good story. If you assume (like I do) that there are many paths to power, the world is still totally consistent.
If I'm allowed to play an Elf then my Elf should in theory be able to potentially do things that any other Elf of the same class and level can do; and further should be able to be the same class as any other Elf in the setting.
And why should all elves have a class ? Why can't you have power without a class ? You know, PCs do not have a class tattooed on their forehead, it's just a gaming artefact that does not have to translate into the game world.
Just because someone in the setting happens to be a PC does not excuse them from also being an intrinsic part of the setting's population; and this is where 5e gets it so awfully, horribly wrong.
Only in your specialised vision of the game, but the game in itself does not have or need that kind of limitation.
Sheer simplicity.
Worlds can be complex too, it's not necessarily a bad thing, you know.
I've already got far too many spells in my system, inventing regional variants for all of them would just add to the mess and also probably take a stupendous amount of time. Deity-specific variants on Clerical spells, which IMO are far more likely to occur, also haven't yet been done for the same reason.
THe nice thing is that you don't have to prepare anything in advance. Just add small things when you feel like it. No one will explore everything that you might have prepared to audit you for overall consistency.