gryphon25

OMG. I can't cope. I have it in the living room at the moment and was planning to mount it in my office.
Guess I'll just have to keep my noise cancelling headphones on 😔

The Kodak 7. 2 actually can power up from grid only, or pv only. So it does not  insist on battery power being available. 

growattspf5000es runs perfectly without a battery but you need to decent solar panels and NO clouds.
Not really recommended/ideal to run like this.
You would rather run a grid-tie inverter if you do not have batteries.

Some always stay on and ramp up. Budgetish ones tend to be louder-er permanently

Battery-less operation is a feature of some inverters,not all

It really depens on which inverter you have. I have the Kodak Hybrid off grid 7.2kW and it cannot start without a battery. Friend of mine has an older Goodwe 6kW grid tied inverter and it can start without a battery.

Correct, you need to size that fuse so you dont overload the rating of the battery,otherwise you ultimately damage it when there is a sustaimed load demand thats above its specification. 
 

One more thing, if you cold start your inverter with the battery,it is not feasible to just close the fuse or breaker to make contact. The internal capacitors takes a huge hiding with inrush current. If you using lead acids, put a 60w incandescent globe over the fuse to allow a precharge of 20 seconds. Then remove lamp and close fuse or breaker. You will notice no arcing anymore. 
If you have a lithium, it has built in precharge, but only if you close the circuit with the bms on-off switch, ie the breaker and fuse must already be closed. 

My take on this is the inverter will look after itself, it has a suitable  built-in  rated fuse or fuse array to protect its internals. 
The external fuse therefore should be rated to protect your battery and cables more than anything else. This will be dependant on the battery size, but the inverter will not demand more than 170A (plus a bit more for surges) so 200A is fine. But this means your battery should be at least 200Ah 1C. 
By CB you mean an isolator? If so, its just there for isolation, not overload protection (the fuse is enough protection) . You therefore select a breaker that can operated at the 200A minimum, but its ok if its rating is even much higher.