No I wouldn't be switching fuses according to load - or at all.
Instead I'd do it this way:
- Fusible link at the battery end of the hot wire, sized to go if the battery wiring gets shorted. (One at each bank if multiple paralleled banks are paralleled at a junction block.) This is more the fuse at the pole transformer (which SOMETIMES keeps it from exploding when overloaded), rather than the mains fuse of a house drop (which doubles as a cutoff for the house).
- Hook the inverter directly to the junction block (with wiring big enough that IT won't catch fire if pulling the sum of the fusible-link ratings on the paralleled banks) and depend on the inverter's internal protection to cover it (unless the inverter manufacturer calls for an external fuse.) If the inverter requires a fuse or the wires to it or its terminals can't handle the fusible link ratings, put the appropriate protection at the junction block end.
- The rest of the minor load circuits get a bunch of fuses in a distribution panel, just like the fuses or circut breakers for the distinct circuits in a mains-fed house. Again they're sized to prevent fires from overheated wiring due to shorts or overloading, more than to protect the load devices themselves (which normally have their own fuses or other protection if they have an issue with hazardous overloading on failure.) And again a fusible link near the junction block end if the wiring from the junction block to the distribution panel isn't up to the sum of the batteries' fusible link ratings.