Different Instruments

See https://en.wikipedia.org/wiki/Transposing_instrument

Couldn't we just put the instrument part and just transpose it to different keys?

MuseScore has the power...

See:
https://musescore.org/en/handbook/transposition-0#transposing-instrumen…
and:
https://musescore.org/en/handbook/concert-pitch

Basically, you can compose your masterpiece with 'Concert Pitch' turned on - so that all staves display in the same key. Thus, it's much easier to visualize the harmony across instruments.
Then, when you are done, turn 'Concert Pitch' off and each transposing instrument will display the proper key signature for the correct reading and playing of the notes by the respective instrumentalist.

Regards.

The big picture / short answer is this:

These different clarinets come from a time in history when a clarinet could only play effectively in one key (a slight overstatement, but only slight). So you needed a different clarinet for every key (much like a standard harmonica today). Over time, that limitation was removed - modern clarients can play well in any key, although some keys are easier than others. So people gradually stopped relying on the different clarinets so much.

The bottom line is - don't use any clarinets except Bb clarinets if you are not an expert in clarinets and know for a fact that the musicians who will play your score have access to one of those more unusual instruments. Create your score using Bb clarinet, write it with "Concert Pitch" turned on so you don't have to think about transposition, then when you are done and you generate the parts (File / Parts, New All, OK), MuseScore will handle everything automatically for you.