As odd as that is, .. i don't think not using their summoners is punishable by itself, Not even if they are well aware of how important they are to their team or if they just completely refuse to use them ever, in any match for as long as they have played the game.
The reason? .. It could ultimately be the way a player chooses to play the game.
As an alternative example, someone could chose to use nothing but Heal and Smite regardless of what lane they are in.
Or they could chose to never EVER buy boots. ..
The game is intended to include these choices, and some people do these things because they enjoy making things harder for themselves.
On the other hand, if they are doing this with the intention of ruining the experience of others, that becomes a problem.
From a punishment perspective, it is difficult to prove what someone's intentions are, HOWEVER, it is VERY likely that they would be doing more than just not using their summoner spells if this was their intent.
I don't fault you for reporting them. It is probably good for Riot to look into this situation to see if there is a pattern of behavior.
Ultimately though, I don't expect that someone would be punished for this reason alone. At the very most, they might receive a warning message that recommends they utilize their summoner spells.