It depends; we (small company/team) do emergency work, especially on legacy software including c++. We usually are at 300-500$/hr but $1000 has happened if the client is desperate and the work is hard. If a company is losing or not making the million$+/day they normally make, they don't care about the hourlies for the fix. We typically go in for a few hours to a few days; we don't take long term projects. Still we have pretty high utilisation.
For collecting the payments we use a factoring agency; it costs a % but whatever; we are always cashed up. And lead generation, well, people find us. I have been 'giving away' this 'business plan' for decades and no one is doing it. Probably because everyone wants to focus on something long term, not jump from php to c++ to cobol to java etc and because of the great resume driven dev strategy. I am for one looking forward to fixing the misery that is nextjs and its 'ecosystem' for the coming decades; please continue! I will have to up the hourlies to 1500+ for that miserable experience though; give me cobol or java any day.