Sure, that's a valid point. Here's my counter argument:

First of all, from my eyes, I think Valve uses little of competitive Dota2 to market Steam. Correct me if I am wrong, but I think the word "Steam" has never been mentioned in the broadcasting of a professional Dota2 game - even though to play the game you actually need to have Steam installed so it's a physical requirement. With this in mind, I think Valve could have used Dota2 as a bigger channel for its marketing, but for whatever reason chose not to (ethical, Valve's perception of value on marketing, its saturating brand awareness, etc.). I think, in an alternative universe, Valve can just fund the prize money for tournaments by itself and more aggressively market itself in the process. Given Valve's revenue numbers and my overly simplified marketing budget calculus, this is not an inconceivable scenario. Again, this will just go into their marketing budget to boost its revenue through its distribution platform.

Secondly - and I am sure this will be controversial - I think the current prize pool for Dota2 tournaments (especially TI) is a bit excessive anyway. While I know Valve sells extremely heavily on the prize pool of the tournaments (and I know the mainstream media LOOOOOOOOOVVVVEESSSS this since the prize pool is super simple to report on), I am not 100% sold on the prize pool being a reflection of the quality nor the health of the competition. For instance, does NFL even have a prize pool? Winning the Super Bowl seems to be more on the prestige - and the money comes indirectly after that. Obviously esport is different and does not operate on the same scale or budget as NFL, but my point remains that I am somewhat sceptical that bigger prize pool brings better and healthier competition. In fact, I think a prize pool of ~2 million dollars (which is comparable to other triple-A esport games out there) is probably sufficient, and ~4 million will topple all current competitions - and that kind of money Valve is probably willing to shell out for marketing if it chooses to.