Add a one-click compile which doesn’t invoke the compile dialog but uses your last settings, these last setting would include the name of the file that you create. This would simplify my work flow.
Your last settings are kept as long as the project is open, so you already have a two-click compile, plus accepting that you overwrite the previous compile output.
You can save your settings as presets, unique for each project if you want. Choosing a preset and then compiling require four clicks, and subsequent compiles two clicks.
Two me it seems like a dangerous concept if it was possible to overwrite the previous compile output without being notified of what you are doing.
For stuff like this I like to look to automation and macro software. This is a chain of events where we’ve inserted very necessary precautions to avoid making it too easy to inadvertently destroy data. If one wishes to bypass those precautions, I think the best answer is to use software designed to streamline other software. AutoHotKey is a popular mechanism for doing so on Windows, and on Mac I use Keyboard Maestro (and in fact I have a macro that does just this: compiles, confirms and accepts overwrite with one hotkey).