When searching in execution history, the search value is used pretty quickly after you stop typing. This means that you have to wait for the search to finish even if you weren't done typing the search string. It also means that if you have a typo, you have to wait for the search to finish before you can correct it. I keep a long history of executed SQL, so each search takes a while to run.

In my opinion, it would be better to have a dedicated "Search" button so that you could submit your search string when you're finished typing it. This should trigger off the enter key as well. That way I can finish typing my search string and just click the button or press enter.

If it's a useful feature for others to have the search run automatically, then it could be a feature that could be enabled or disabled. For example, I would want the auto-search turned off, but others may want it turned on and set to a certain time-delay, like 5 seconds.