SB13 and its grace period on unpermitted units should preventing this from occurring.  

If I let them run loose it would probably be 5k-10k a year in unnecessary costs.Also the work does come in spurts so it isn't consistent.

Or is it simply cosmetic or preventative or an upgrade?

Often times inspectors overlooked them as they are very small and minor but as you can probably already tell, they are extremely important and prevent water intrusion.Your best bet would be to contact a very reputable Siding/roofing contractor and have them go through the entire property and put in the proper drippage flashings seals and caulking necessary and have them insure the work. 

Will this prevent me from saving for the down payment for the future house?

This prevents Amy confusion about different leases, agreements, etc.

As others have stated, a well-drafted LLC operating agreement should have language that would prevent management from withholding material facts and/or removal provisions for a manager who doesn't comply.

Okay gotcha thanks for that rude and unnecessary comment...

Insurance is to prevent loss, not provide profit.  

If you are in a neighborhood with a higher crime rate (C neighborhood), make sure to protect the AC units by putting a cage over them to prevent theft.