I tend to defer to those here with more years experience but in this case I have heard it from more than a couple of college coaches that they like kids to have some other sports interests. First it was my lying eyes and now my lying ears?
My understanding was playing other sports develops different muscles and abilities. Plus the letter jacket is more impressive with the extra patches.
AS to the OP, it sounds the tourneys are more than run of the mill and I'm glad DD's season ends the day before BB tryouts.
My DD has talked with maybe a half-dozen college coaches who have expressed serious interest in her. The only non-softball activity they've ever asked about is academics.
Sure, coaches like it. But that doesn't mean you should do it. College coaches would rather have a great softball player who specializes than a pretty good one who plays multi-sports. Fact that college coaches might like multi-sport athletes would not factor into my decision to keep playing another sport. Reason to keep playing another sport is you like playing another sport.