I have used USB SSD enclosures and even a USB NVME enclosure with great success. This includes RPi 4b and RPi 400.
But, I have a powered USB hub that I connect the USB Keyboard, and USB Mouse to. This eliminates the power drain on the RPi 4 power supply for these devices leaving more power for the RPi and the USB enclosure.
Plus, I do not know exactly how these powered USB hubs work.
Is there a current blocking device which does not allow the USB hub to add additional current to the RPi’s current? I don’t know.
I do know if the USB hub’s power supply is not plugged in (or not powered from the power strip, don’t ask how I know this) the RPi’s power supply runs the keyboard and mouse in the USB hub.
Anyway, the point I am making is be sure the RPi 4’s power supply has enough power to run a USB SSD enclosure, plus keyboard, plus mouse and of course the RPi 4 itself.
Pudge
EDIT:
Here are some of the devices I have tested. The one on the far right is the USB NVME enclosure.
The problem with a borderline power supply is it runs fine on low CPU and/or GPU loads. Then gets flakey when a CPU / RAM/ GPU intensive app runs. So it can be intermittant.
Here is a good topic on this