Arpie:the more hits, the more balls you have to buy. Increase the number of lip-outs and putts missed by an inch or less and increase hits.... thus head to the pro shop to buy more balls.
as noted, putts don't effect ball hits (this has been tested and confirmed pretty much), but that doesn't account for all of the scenarios that impact ball use or why the theory has came about.
That said, I will say, your theory is also heard or referenced to the seemingly higher number of "forced tiebreaks" in mobile coin games, where the tie break does consume more ball use.
Remember- the game stats identifies average distance to the pin in your approach shot - so CTTH stat is already available to determine who won - without going to another tie breaker shot. But, sending you to tie breaker - rather than using that stat over 1 3 or 9 holes - does consume more ball hits - even though a stat is available to determine essentially the same thing. So yes, it can feel like - in some aspects - the game is designed to consume more unnecessary ball hits to perpetuate more ball sales.