Because Google controls the vast majority of phone manufacturing on the planet: They have to approve every new hardware model. I think if Google said it was dropping support for Qualcomm in new models of phones unless an extended support lifecycle was reasonably offered, that Qualcomm would respond with "okay, bye".

Google likes to hide behind "the OEMs make those kinds of decisions", but it's not reality: The Android MADA still gives them complete control of every Android hardware platform sold with support for Play Services.

And, considering Google is one of the three most valuable companies on the entire planet, sitting on massive piles of cash stashed everywhere they can possibly stash it to avoid paying taxes.... Google can afford to pay for support if it wants to.

If Google wanted to support phones more than three years, it would do that. It doesn't want to, and it's time to stop pretending otherwise.

Google leveraging its control of android to extract better terms from Qualcomm for the Pixel business would be a blatant violation anti-trust statutes and they would get demolished in court

Considering how blatantly Android is already violating antitrust statues (the Android MADA mentioned above which governs the relationship between Google and OEMs is... flagrantly illegal, and has only gotten away with it by being kept very secret), I am quite doubtful that the government will yet do anything any sooner because Google chooses to support users better.

It would not be leveraging for the Pixel business either, it would leveraging Android for Android as a whole: Presumably Google could drop support for hardware that does not provide five years of support from the Android codebase. It would then be on Qualcomm to either meet or fail to meet that requirement, and set their license pricing accordingly.

Having a support lifecycle of at least five years is... bare minimum for the industry. Nobody could argue that it is an antitrust issue to require it.

What kind of market share does the Pixel business have?

Yeah exactly. Both google and qualcomm benefit from this arrangement. They might "blame" qualcomm but they're not going to go out of their way to try to change the behavior and therefore make less money on phones.

Google is the one selling you the phone.