I agree that adding wizard levels to a dragon is a good change and makes it a better monster and a better villain. I just don't think it's a negligible change the way the DMG does.
I wouldn't say that it makes for a better monster; better can only really be determined once you apply a purpose.
If the purpose is to be a greater threat in combat, then I think it doesn't achieve that goal and is therefore not better.
If the purpose is the ability to be a recurring villain, then I think those magical abilities can certainly help.
If the purpose is to make it a better plotter and schemer type of villain, then you really need to add more than just a couple levels of wizard to make that happen (you need to get to the good information gathering spells for that).
In a similar manner, adding a level of fighter or rogue really is not going to help either. As I see it, adding levels of fighter to a high CR monster is a waste unless you are going to give them at least enough to get the first subclass abilities.
But, to roll this discussion back around to monster PCs, consider the adding of monster abilities to characters.
Since I am currently working on a homebrew medusa race, let's look at the medusa as listed in the MM. We are talking about a CR 6 creature with relatively few special abilities: petrifying gaze (this is the big one), snake hair, and darkvision. I am not counting multiattack as a special ability that the character would inherit; I am counting it as effectively being part of the creature's class-replacement abilities.
Darvision isn't really an issue (a ton of races have it).
Snake hair is good, but I don't see it as being any better than a damaging cantrip delivered via a melee attack. I would also consider the MM Medusa's ability to use it as an attack instead of as an action as part of its class-replacement features.
Now, the elephant in the room is the petrifying gaze. How can that ever be appropriate for a PC? Well, the ability gives an out that just about everyone is likely to take (the averting eyes option). So, unless the target is forced to look at the medusa's eyes the ability equates to imposing disadvantage on some enemies within 30 feet (enemies behind the medusa most certainly wouldn't face the disadvantage problem).
This seems to be a very strong ability, but the ultimate question is one of scaling. What if the medusa's petrification DC never rises above the 14 listed in the MM entry? Beyond a certain point, most enemies are going to make that save (Con score, so far as I've been able to tell, is one of those stats that really tends to rise as CRs increase), especially the ones proficient with that save. And, the 30 foot range means that many monsters will be able to engage the medusa before its petrifying gaze can come into play.
I would consider that adding all three of these abilities to a character that is at least 10th level would do next to nothing to increase the power level of that character.