Please charge money for the game...

Personally I also think this would probably be a good idea... or well, a part of it.

You are completely right that setting a paywall would likely deter some cheating.
Though I think it would be good to expand on this, and do something more like what CS:GO/CS2 has done in the past.

They added a "Prime Queue" system, which basically made it so there were 2 queues:

• F2P Queue (F2P Players and users who disabled their Prime Queue could use this queue to get into lobbies)
• Prime Queue (Only users who have spent x amount of money on the game get access to this)

This basically introduced a paywall to deter cheaters from entering paid lobbies, which would lower the amount of cheaters overall in the paid queue.

This isn't that bad of a model, considering most users already have spent a certain amount of money and would automatically get into the prime queue if they ever were to introduce it.
Buuuuuuuuut.... it does come with it's problems. The F2P users would see an inflated amount of cheaters in their matches, as a lot of users are playing in the prime queue instead. Which probably isn't something you want either.

So in that case just making the game paid could be a choice instead of those queues. But you can't really take the game away from people who have been playing all this time. And making all free accounts transition could be problematic too, as some users might already be stockpiling accounts in-case this ever happens. Which could make the "Black market" where users buy/sell accounts bloom more.

Each solution has their own problems, and of course it's the jobs of the developers to look into these kind of solutions. Though with making the game paid in some shape or form, personally, I'd assume some kind of backlash.