Aside from spectating support, I think a major step towards esport territory would be working heavily on the matchmaking system. Currently it's far too basic, and heavily depends on both teams being good-willed and cooperative. if this game truly reaches a bigger audience, all that is going down the drain. There would be griefers, queue droppers, ghosting and all that.
Things I would love to see in this regard:
1- Join as a team. This is just pure quality of life. Let me put together a party and join games in batch, all of us in the same ship(s).
2- Rank based matchmaking (as part of ranked games) backed by a ELO system or whatever.
3- Not seeing what your enemy is picking on the preparation screen.
4- Leaver punishment (sensible punishment obviously, but it is necessary). I really like how Smite does this, and I would do it similarly: There is a passive bonus that keeps compounding as far as you never leave a game, until 100%, in which case it gives you a substantial reward in points after each game. If you leave once it resets to 0 and puts you on a rejoin cooldown.
5- Reward system aside from achievements, such as costumes, flags or ship decals for reaching higher leagues.