Just gonna throw this out here - the physical tournament standard for ESL is probably the least-concerning of the way this is run. People can get extra sticks/pads as needed, or borrow or share.
Why do the online qualifiers have to be platform-specific other than for promotional/exclusivity deals that the players get nothing out of? If you need to have lets say, 50 top players make it out to the finals, divide the number of entrants for each platform based on representation by population - if 60% of people sign up on Xbox One, have 60% of those 50 spots be given to Xbox One users. If its 30% PS4 users, give the top players from the PS4 qualifiers those 30%, and the rest PC (just throwing these numbers out there as an example).
The issues THAT could create is people could specifically avoid playing each other based on platform, or perhaps some platforms might have more killers in it than others. To which I say, this is an online qualifier anyway, and the quality of who's going to make the physical tournament is already incredibly suspect.