FCPX keeps on crashing when starting

If FCP X/iMovie start behaving unexpectedly in any way for no apparent reason, the problem could be caused by corrupt preference files. 

The cure for this is to delete the preferences. 

 Hold down the  Cmd and Option keys as you launch FCP X/iMovie and a window will appear asking if you wish to delete the preferences. 

Click “Delete Preferences” and FCP X/iMovie will open in the default (as-new) mode with no projects etc. on the interface. 

You will have to navigate to any project you were working on and reopen it. 

Deleting preferences is completely safe and because of its simplicity it should be the first thing you do when troubleshooting.

You should generate an EtreCheck report using full drive access from the application preferences.The application is a free download from the App Store. To produce a report use File->New Report. Then use the copy report function and paste it using the Additional Text button in the reply box.. 

Furthermore you need to run the series of troubleshooting strategies listed here . . . starting off by resetting the preferences (and not as the eleventh thing to try according to this list).

https://support.apple.com/en-us/HT203477

You didn't mention deleting the preferences, you merely said you had trashed the application.

The preferences are separate from the application.

You have a ton of stuff you can't be using any more, and a lot of junk. The system's in bad shape and really should be rebuilt. I would recommend wiping the drive, reinstalling the OS, migrating only users if you have to, and then reinstall just the applications you work with.

If you can hang on it’s not a bad idea. I always rebuilt with a new OS, but it’s at least a month out I would think for Big Sur.