I agree with you both. I want a more fleshed out PvP gamemode. Laser Tag does fit the bill to a degree, but the system of running to a charge station between deaths plays better in a team environment than 1v1s. Also the forced team mode leads to unbalanced teams too often with the current population. It is FPS PvP in a relatively pure form, it just isn't ideal and doesn't offer much depth either. An Arena shooter with a variety of over the top weapons sounds ideal to satisfy this.
However Turret you're correct Shooter games make up a lot of the Tower activities, and more variety would help the game feel more balanced in gameplay options. Its obvious from the poll current players are very interested in a Kart Racer, and I'm sure it'd draw in a lot of players as well.
I think the issue here is when Tower launched you had good variety between the four available game modes, but two of them (Virus and Planet Panic) felt rushed and unpolished in comparison. Once Weapon Predictions was implemented to fix Virus the team had a great system to quickly build new games from leading to more shooters coming first.
Once core systems that influence the overall game, such as living lobby/workshop/achievements, are implemented I think the team will have more time to dedicate towards new systems which will lead into the more mechanically different game modes coming to fruition. Keep in mind this is me assuming a lot and just my opinions.