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.
