Independent Sponsor with committed funding for a single deal

I have been thinking in the pros/cons of an independent sponsor vs. a private equity fund for lower mid market deals.

Has anyone seen any firms that follow the independent sponsor model but have committed funding just for the next deal even before an LOI is signed? After closing the deal investors would be asked to ”refill the pot” for the next one, but they can always opt out and the team would need to find other investors to fill the gap.

This should allow enough credibility to access deals, given the availability of funding, gives more flexibility to the investors if they want to stop investing in the space or no longer like the team, would avoid the double negotiation before signing in the independent sponsor model (with both the LP investors and the seller) and at the same time should be easier and faster to raise than a fund and allows a more prudent approach to investing by the team given there is no pressure of a large fund recently raised. It also allows more scrutiny by investors than the traditional PE model (but not as much as in the independent sponsor model which in my view damages the chances of closing deals).

Obviously it also has drawbacks but would be great to know your thoughts and if anyone knows any existing firms following this model.