We should be thinking of ways to improve the situation for everyone (not saying I have the solution), but personally (and unfortunately) I don't think this would have any impact.
What's Google's incentive to protect your privacy, and what are the consequences if they fail to?
Compared to a firm that is marketing services on the proposition of privacy being at the core, the risks to Google's business, reputation and finances are likely minimal.
Whereas, if one of the firms that markets providing services focused on your privacy is found to be intentionally and wilfully violating that, it ceases to be a violation of trust and becomes a violation of contract, false advertising... essentially fraud, and the consequences of deliberately misleading and defrauding customers is more significant than an accidental (or wilful) privacy breach by a corporation that openly markets itself as not respecting its users privacy.
If Protonmail fucks up, there's not going to be a NYT article about it.
If google screws up, they might see a small blip in add revenue before recovering.
If Protonmail screws up, then they'll lose paying customers which is their only source (presumably) of revenue.