@Filip Reutov the universe has a way with timing.....I just finished Mike Butler's "Landlording On AutoPilot" this morning and I felt like i could hear him scream "No" lol. All kidding aside, any perceived benefit holds no value if something goes wrong, including what others have commented. Perhaps look at it this way:
If you were going to build said shed what steps would you need to take - Permitting, materials selection, time, updating your insurance policy?, possible survey, etc. Now assuming you'd allow the tenant to construct this shed, which is the same as going into an agreement with a contractor with appropriate skill do you expect/know if the tenant has similar skill, licensing and insurance?
Now let's say the tenant is in fact licensed and insured. Are you prepared to give him the job as a contractor and not as a tenant doing you a favor - proper quote, expectations, etc? If no, then you're risking losing a tenant and incurring unnecessary expenses. If yes, there exists an element of managing him/the job which could get tricky especially if he thinks he's doing you a favor in the long run.
Continuing the "favor" angle, do you think you'd be able to charge the tenant(s) for the additional storage, similar to garage access, basement storage, etc.?