What's the problem with this exactly? Doubling synonyms is a standard way many languages construct words.
- Pathway (path + way)
- Courtyard (court + yard)
- Safeguard (safe + guard)
- Nonetheless (none + less)
And it's not just English:
https://websites.umich.edu/~duanmu/Diachronica99.pdf
Group and set are not complete synonyms. A group is a number of things. A set implies that there is some connection between the things. If you have a group of silverware, it means you have a bunch of spoons in a drawer. If you have a set of silverware, it means you have a curated collection of spoons that were manufactured to be used together.
A groupset is a number of things that have a connection to each other, meant to operate as a complete system.
+1. Well reasoned. I made a similar point dozens back, but you said it better, particularly about double synonyms.