The English Rule makes litigation inherently higher risk for less wealthy litigants while barely limiting more wealthy ones, and further tips the balance of the legal system to the wealthy. And it doesn’t address the need for QI.
OTOH, QI would be fairly comprehensively solved if the immunity was treated as an indemnity by the employing government rather than a simple immunity, such that, should QI be established to apply, instead of the case being dismissed before reaching the merits, it became a case where any damages would be the responsibility of the employing government agency rather than the employer, bypassing any otherwise-applicable governmental immunities. (The logic of QI is that it is unjust to hold a government employee responsible in their personal capacity for a violation of the law done in their capacity as a government agent, within a zone in which they had discretion in the job, and where there was insufficient basis for them to know that the act was a violation; there is, I think, a very good argument that this is the case but that the result should not be that all remedy is lost.)
The problem is when governmental immunities stack with personal immunity under QI and with insufficient prosecution of crimes by public officials to denial all remedy, not with QI alone. In fact, I would argue that QI is, alone, the least important of the three roots of the problem, just that it prevents the last available end-run around the more important ones.