I play anivia, aurelion and talon mid. And well, velkoz just spams abilities constantly, like without an item. it's kinda crazy 1-3. Not exactly gamebreaking bc they're dodgeable, but based on the damage+combo potential what the heck?
I'm not exactly sure what you want to define as "too much" mana efficiency, but I would like to point out that the three champions you specifically noted are heavily balanced based on their wave clear, whereas Vel'Koz's laning presence comes primarily from his poke. If Vel'Koz had the same "mana efficiency" as Anivia, Aurelion, and Talon, not only would he have to deal with the fact he's going to get outpushed by these matchups in the lane where priority is arguably the most important, but he also has to deal with the fact that his primary forms of poke are, as you pointed out, rather dodgable. This is opposed to the fact that wave clear is incredibly reliable since minions don't intentionally dodge skill shots.
In other words, for any individual uses of their abilities, Vel'Koz's Q+W Waveclear is lackluster compared to Anivia's Q+R (granted, pre 6 discussion but still a factor), Aurelion's P+Q, and Talon's W+Tiamat. Vel'Koz must then approach the lane with his element of Poke, which I think we can all agree is at the very least much less reliable than Waveclear in and of itself. Again, I have no stance on what you consider as "too much" mana efficiency, but is it possible that for Vel'Koz's lackluster wave clear and less reliable poke he should have more mana efficiency to balance everything out?
It's not casual that as a "support" he can perma-spam. Very fun to play against :P
Vel basically has no mama issues throughout the game as long as he gets the occasional Q refund.
He just has really low mana costs.
He also had a pretty terrible early game and a weak ultimate to anybody with some bonus hp, a shield, or some decent mobility. Even then, sitting in his ult doesn't kill anybody who isn't a marksman really. On top of this every single ability is a skillshot, each of which is pretty easy to avoid. Can't believe you're bashing Velkoz and not champs like 
first who do just as much (if not more) damage but is also easy-to-land, bigger AOE, or overall a lot more forgiving to play with a mana pool/regen that makes misses pretty forgiving.
Every single champion spams spells. Champs dont run out of mana anymore.
He has a mana refund mechanic like Annie's, except he gets a 50% refund on his Q for each kill. His Q can hit three targets, so he is able to get a 150% refund.
Although, his waveclear to get that 150% is pretty much just autos/W. Aurelion, Talon, and Anivia are all much better at waveclearing.
Play Velkoz vs skillful 
W spam and then say he has too much mana.
great wording. i recognized this too already but if i would have made a post like this it would get flamed and downvoted. but yeah, i agree with your point of view.
i always run out of mana early [zombie-brand-mindblown]
Never knew why he's not popular. He outclasses most midlaners in terms of waveclear and damage, and he is quite easy to play. I'd rather have a vel'koz on my team than a Xerath/Azir/Syndra for example.
On the other hand, Vel'koz has kind of puny damage on his abilities. His main source of damage is his passive, which needs 3 spell hits.
And nobody is going to blame you, if you run sustain runes against a poke composition as ADC. Most poke champions really benefit from the enemy using the same runes every time. I barely saw any ADCs run resolve as secondary tree, because Second Wind and Fleet Footwork + Revitalize make it sure that it's going to be incredibly difficult to force you out of the lane. Instead most ADCs grab the same runes all the time (sorcery and inspiration), which could maximalize their damage output, but in reality their main source of damage is from items and the runes they mostly pick only start having some serious effect after like 15 - 20 mins. By that time you could farm at least one item and a boot if you aren't forced out of the lane constantly. And even if the runes are not enough, one lifesteal item just makes it literally impossible to force you out (khm khm 
)
If he chooses wave clear then he maxes W first and will have no mana efficiency. Q does return mana, but requires set up. Then you have to ask, is velkoz spamming abilities to clear the wave, or poke the enemy? If its to clear waves, then q can give back some mana, though at best you'll break even most of the time because minions move around a lot. If its to poke the enemy then he'll run out of mana quickly and have to back.
I play anivia, aurelion and talon mid. And well, velkoz just spams abilities constantly, like without an item. it's kinda crazy 1-3. Not exactly gamebreaking bc they're dodgeable, but based on the damage+combo potential what the heck?
His Q regains 50% of its cost per minion killed with it, making it so that you can even regain 150% of its mana cost if it last hits minions. Basically, you have to force good velkozes to not use their Q’s or other abilities in an optimal manner.
Okay, so all I really do anymore is play Vel cuz other champs are pretty boring to me. Q requires more time and setup compared to most other champions in the game, as listed in above comments. Support Vel also takes a massive hit seeing as how everything can be dodged rather easily and his ult can be countered with basically anything. W is pretty good for waveclear, but unless he has 
theres nothing he will be able to do after casting it a few times. E is a knockup, so that won't be used for any harass or waveclear anytime soon unless hes about to miss a cannon. So if he manages to get that, then you're right, he will spam and has unlimited mana. But think about it...
So many champions that can do his job, but better IMO in support, but most of these champions could also do it better mid too. Only the base damage is different and the mana costs are slightly higher or less.
This is also how I feel about 
Very mana and cooldown efficient and usually end up making your lane super uninteractive due to very small windows to trade.
I noticed this too and idk why riot never nerfed since its too op on botlane. I can't seem to enjoy adc when vel spams abilities nonstop and never run out of mana
