I do not believe the people posting on this forum are a representative sample of all the people playing D&D and I do not believe their reported experiences are congruent with the majority of people playing D&D.
I stand by what I said - I do not believe Wizards are a problem on the majority of tables and there is no objective evidence to refute that opinion. There are lots of anecdotes, but that is all.
By the way, I have been playing D&D since 1980, which beats your 20 years by more than double ..... not that it matters to this discussion.
Yet shouting others down is exactly what those who claim there is a problem with Wizards are trying to do. I readily admit that Wizards are a problem at some tables (which I believe are a minority), based on the testimony on this thread and forum.
However, there are other people on this forum that use superlatives like "this is why Wizards dominate every encounter" and "Players can't have fun with them in the party".
Both of these statements are objectively false, they are not a matter of opinion, yet those that say them get upvoted as if they were true statements that were somehow relevant to this discussion. This represents the epitome of shouting others down and trying to use the popularity of an argument, and a factually false premise, instead of using reason and the underlying logic of the argument.
Finally, I will note that homebrew and choosing/limited magic items are easy available avenues to nerf a Wizard to meet your needs if this really is a problem at your table, and these are both generally easier to do mechanically than it would be to go the other way and add back in mechanics for things that are removed.
I concur.
While I started the thread, I recognize the issue for myself is I prefer low-magic games, and too many spells, too wide a variety, constant cantrips, etc. is directly opposed to the style of game I like. So, in many ways ALL full-casters are an issue, but Wizards just happen to be the worst offenders in that way.
Wizard (or any caster really) do not dominate every encounter, trivialize every challenge, or prevent other players from having a lot of fun when they are in the party. Now, they can certainly do A LOT and as nearly always the DM, the default magic level of 5E does make challenges which would be difficult for martials much easier for wizards.
For example, an exploration challenge of a chasm. Martials would either have to take time (and risks) climbing down, crossing, and climbing back up. A caster with
dimension door might be able to reach the other side with a single spell.
Higher level spells can change the entire swing of an encounter in ways martials simply can't match. Limited spell slots is a poor balance point for such power, however few games ever reach this point, so I can't say really how much of an issue it is. For me, the simple fact it is
possible, it a problem.
My solution (as new home-brew) is to slow down the spell progression of casters so full casters cap out at 5th level spells and half-casters at 3rd level spells. Cantrips function on a recharge, so aren't at-will. I've also revamped the spell lists so wizards have fewer spells. There are some other changes to make it more gritty, but those changes make it low-magic for me.
Is it anecdotal to say that Wizards have both more ways to, and much more impactful ways of, do things in general?
More ways? No, it isn't anecdotal. It is right there in the size of their spell list---but it also depends on what they are trying to do.
More impactful ways? Entirely depends on what they are trying to do.
Even if you ask:
more things they can
do? Now it depends on what spells they have access to (and much of that is DM fiat).
IME, if you are happy with the default "magic-level" in 5E, there really isn't much of a problem with Wizards until you reach tiers 3 and 4. By that point, they have both large enough variety of spells in their spellbooks to be generally well-prepared for most encounters and challenges while also having sufficient spells slots to cast the necessary spells when needed.