I mained Vel'Koz for most of season 5 from mid plat up to mid d4 (about 500 games). In a perfect world Vel'Koz remains exactly the way he is now, his play pattern (HUGE wombos, godly kiting and teamfighting, very strong lane control, solid objective control, HIGHLY underrated poke and siege) is very enjoyable and satisfying. I understand that Riot have their own motivations for reworking champions and that's fine. It's true that his vulnerabilities (self-root ult, immobile, relatively low utility, etc.) make him a lower priority than other mages that perform similar functions, so I can see why the devs think he needs something to make him strategically advantageous over these alternative picks. In principle I like this idea, but I worry Riot are going to gut his waveclear (which is the key element of his kit that makes him even playable at higher levels, it's actually the key element of any mage's kit that makes them viable at higher levels, imagine any of these if they didn't have highly efficient waveclear: Viktor, Lux, Syndra, Ori, Ahri, etc.) and give him some cutesy gimmick W that offers highly situational damage. Overall though, the tone of this OP keeps me optimistic.
Aimless diatribe aside, there were a couple of troubling things mentioned in the OP about Vel'Koz's play pattern.
poor scaling
When purely considering his damage, this is simply untrue. While it is the case that Vel's ult and E AP ratios are relatively low, his Q's ratio is good and his W's is good when you get both hits, which will be happening consistently in teamfights, and with experience in skirmishes and 1v1's, when you get a WE or WQ the double proc of W plus the true damage PLUS the Thunderlord's proc actually does quite a lot of damage even to tanks late game. I say this purely from experience. What's more, Vel has very little trouble hitting the backline in teamfights with at least one tick of W and his ult if you save your abilities for the appropriate moments (a valuable skill on any teamfighting mage). True damage, TLD procs, magic penetration, and liandrys destroy the squishy backline. In principle and practice Vel does A LOT A LOT of damage in teamfights at all stages of the game. The only concession I can make is that he, like many other immobile mages, is vulnerable to divers with lots of hard CC (Nautilus, Malphite, Leona, Alistar, Zac, etc.) and assassins to varying degrees. And to that end, late enough in the game he can be "outscaled" by certain picks that take enormous advantage of his weaknesses if one isn't careful enough. In short, Vel's damage scales VERY well into the lategame, he can handle tanks with TLD procs, true damage, and Liandry's burn and his range and AOE along with skillfully placed Q's (not actually that hard to land, with experience) allow him to be a meaningful threat the the backline.
laning pattern involves mindlessly wave-clearing with W
This is not entirely true. With 15 AP from runes you can clear the the whole (non-cannon) wave with 2 W's with 3 points in W (level 5). It is possible to do so, but this requires one to walk up to the very edge of your melee creeps to get the perfect alignment, thereby allowing your lane opponent to push the wave and land harass on you simultaneously while on their end it is very easy to dodge Vel's W's if they aren't accompanied by an E or Q. Thus your lane opponent is more efficiently using their mana than you, and you will eventually get forced out of lane. If one opts to W the wave at a safe angle, 1 or 2 cs will usually not get hit by the W or only get hit by one tick of it, meaning that if one chooses to play as far away from the wave as possible and spam W's on it WITHOUT trying to trade with or harass the enemy laner then you will eventually go oom and accrue a cs deficit. So yes, it is possible to just spam the wave with W's and get enough gold to be relevant because of the high base damage on ult and true damage, but this is NOT the optimal way to lane with Vel and will not get you the most gold possible out of laning phase.
Vel's spells can and should be used aggressively in lane. The damage and slow from Q is very important in setting up WE's/EW's and can be done consistently with practice. It works like any ranged lane matchup, you shoot your spells and throw autos when they go to last hit. WE is an incredibly powerful trading tool (particularly now with the true damage and TLD proccing simultaneously). Because of Q's low mana cost, it isn't very risky to frequently look for Q's that set up WE's or just for lane poke: Q is a very valuable tool in lane.
In fact, Vel should only be using 2 W's on the wave when his opponent is hard shoving or he is very far behind (when one is too far behind to straight up fight in certain matchups, all one can do is double W the wave, I will concede this to the dev team). Vel has enough waveclear to make it SAFE to be aggressive in lane: he can waveclear defensively nullifying attempts of lane opponents to burn his farm under tower, thereby forcing them to consider leaving the wave up to deny cs by trading instead of shoving. In summary, there is much, much more depth to Vel's optimal laning pattern than just W'ing the wave twice after it appears.
Generalist damage output without meaningful utility means he must be balanced around simply doing more damage than anyone else
I somewhat addressed this above so I have less to say here. Vel'Koz does, A LOT, of damage, I really don't understand where this perception comes from that his damage is lackluster compared to his peers. From 250+ games around low diamond I can say this with high confidence. I will concede that his utility is relatively low, but again this is overblown. He has AOE CC in his E that knocks champs away (I cannot understate how strong this is in practice both in peeling for Vel himself and teammates as well as for making picks from fog, not to mention it's wombo setup in teamfights and synergy with other knockups [I know Vel E is suspension] like Sion ult/Q, Zac E, Malphite ult, etc.) and a highly spammable slow in Q that is near impossible to miss when kiting. Also when Vel ults from a favorable position in a favorable situation (enemy doesn't have any cooldowns that cancel his ult), the slow across the entire enemy team can be a very strong setup for your team. I don't think he has to be balanced by receiving more damage because I think he already dumps out insane amounts of damage and has quite a lot of CC.
And that's all I got. Very sorry for the ramble (upon reread, this has less focus than I originally intended), but hopefully I made some points worth considering. I think Vel is highly underrated damage-wise mid-late game, he feels very unique and fun to play, I don't think he needs to be changed in any way (but I am certainly open to concrete suggestions about gameplay and strategic niche changes, rather than design and thematic goals), and his laning phase (optimally played) is no where near as shallow as it seems is being perceived. Thanks for reading anyone that did.
Edit: Fixed some grammar, filled in some missing words, added and changed a few words and phrases to better clarify certain points.