I just realized that Swain is a master Tactician, In fact one of the best. And, each summoner represents each city. So really, Why isnt Swain a summoner and commands the Noxian troops on the field, instead of participating himself. I assume, that each summoner is carefully picked from each city and are the best tacticians out there. Why, was swain picked to enter the battle instead of doing what he does best.

Tl:dr Swain should be a summoner not a soldier.- he is a tactician.

Bump

My guess, and this is only a guess mind you, is that he is both too powerful and too interested in personal goals for them to consider recruiting him.

Swain made it clear in his League Judgment that his goals are personal. And the summoners of the league can't have such personal ties to the outcome of the world. They are representatives of their nation is they represent one at all. Not the ones who decide what goes on for their nations.

again this is just a guess. I'm not the most versed in LoL Lore, but I'm pretty sure that's how it works.

Most Summoners fight for personal goals. So that argument doesn't really make a lot of sense.

It is entirely likely that he simply doesn't know summoning magic.

Swain is an old mage, and summoning is just one of the many, many forms of magic that exist in Runeterra, and it only became of particularly great importance some 20~ years ago. It is entirely likely that he is simply not trained in it, the same applies for the vast majorities of other mages.

Still, to be a league summoner now, you need intimate knowledge of high level summoning magic. If Swain's specialization as far as magical arts go doesn't include that level of summoning magic, champion is basically his only option.

Don't forget that being a champion also meets his personal goals better than being a summoner. Summoners are, by and large, faceless as far as the public is concerned. He doesn't just need influence, he needs exposure. To be ruler of Noxus, he needs a powerful public image and a following.