Have a look at the field definitions in "Options > Library & Folders > Manage Library Fields". You will see most dates are in "Date" format, which is the numbered format you are seeing. I think MC uses the standard number format that many applications use. i.e. 01-01-1900 is 1 or something like that.
Only the [Date (filename friendly)] field is a simple string. A lot of the Operating System dates are marked as "Unknown", but are actually still recorded in this "Days since 1900" format.
If you want to see what is actually in the fields, create an Expression column in one of your Views, and enter the expression [Date,0]. The ",0" means: Show the raw data.
So, the problem isn't with MC, which is storing dates in a standard and accepted format, but with dbPoweramp, iTunes, and MPC. Maybe you can get them to read the format correctly. It may be a setting. It may be as simple as telling those applications that the field is a Date. Or another solution would be to just stop using those other applications, and only use MC!
If you really want those other applications to show the date correctly, do some research into storage of dates in applications, and specifically in those. After all, people have been sharing metadata between MC and lots of applications for a long time, and it has always worked. So there must be an easy way to make then work correctly.