KEEP IT CLEAN AND DRY!
I don't want to worry you, but I know of a saxplayer who used to keep his reed/mp together all the time for ages ... when he did have to change reed there was a horrible build-up of gunk and yucky stuff and I swear there were things moving. Ewwwwww
No point in sterilising everything, just dry the reed, dry the mp, se pullthru on crook - there's mops for mps and crooks, but I'm not sure if they're better than letting air get to those pieces ???
For those of a strong constitution ....
THE PRESENCE OF CLINICALLY SIGNIFICANT BACTERIA WITHIN BRASS AND WOODWIND INSTRUMENTS
If that's not enough you can read about Hypersensitivity Pneumonitis - Sax Lung (Antigen source - mouthpiece, probably antigen - Candida albicans) here ....
http://www.moldacrossamerica.org/HP%20lesson%206%20PCCU.pdf