I have a Vega64 watercooled card in a Sonnet Breakaway box and have been running it for around for 2 and a half years.
Another Vega64 Strix in a Razer Core enclosure with 600W power supply, then a Radeon 7 in another Breakaway box.
I have had absolutely no issues with the eGPU or card working fine, the only issues over the years has been occasional driver issues in the middle of beta macOS updates.
If I get some time later I can put the eGPU on a Kill-a-Watt meter running a worst case scenerio stress test or benchmark and show the actual power usage.
On some of the sub-600W power supplies earlier on, the manufacturers were cautious with their recommendations because many people would also be drawing power to charge their laptop as well as GPU usage and those particular boards did not delivery very much power delivery.
Putting a larger power supply will not change the power delivery, it is a limit of those boards on those model eGPU's. So if you are wanting max power delivery and GPU usage, choose an enclosure with a higher rated power delivery.
If it will be connected to a desktop or the laptop is under it's own power you're fine. Even with the low power delivery you're fine, the laptop will just not be able to get enough power to keep it charged for a sustained amount of time.