I've heard it's the buss bar that's limiting, not empty fuse locations. Say you've got a hundred amp service with a hundred amp main. Add twenty amps from the PV panels. The buss bar could overload.
Looks like you have a 4/12 roof, just shy of 20 degrees pitch.
The rule is you cant connect more than 20% of the rated circuit panel bus rating. Unless you have an odd panel, the buss rating is usually the main breaker rating. Most homes have 200 amp main panels so that means that only 20% of the 200 amps can get connected for a total of 40 amps which is roughly 9 KW of panels. If on the other hand the panel is 100 AMP panel its down around 4 KW. In that case the panel can be upgraded to a panel with a larger bus rating. The service entrance doesn't need to be upgraded to do this and actually there is an advantages to it if the main breaker is kept at 100 AMPs but most folks would go with a line side tap that connects into a new box located between the panel and the meter and leave the panel alone. The problem is that the electricians usually are subcontractors who bid the work low they try to make up the lost profit by selling extras so things like panel upgrades adds a lot of extra profit n their part.
The potential unexpected cost I didn't mention that surprises folks is that the roofing really should be new or near new under the panels. Its not required its just a practical decision in that once the panels are down reroofing is a PITA as the panels need to be removed. If you have a recent 30 year roof and new solar panels odds are someone else gets to worry about it. BTW, some folks deduct the reroof as part of the installation, its definitely one of these see your tax advisor situations but I personally wouldn't want to be audited on it.