Not asking too much from the battery, but asking too much from the solar panel.
Figure that 12w panel can replace 1a per every hour of good strong sun. If you move it around to keep it aimed at the sun, you might get say 6 hours a day. So it's replacing up to 6 amp*hours a day.
It doesn't take much to drain 6ah out of the battery. That's a 2a load for 3 hours or a 4a load for 1.5 hours.
With a small solar panel, what usually ends up happening is not that the solar will keep up with the loads, but that it just helps mitigate the loads a bit to extend the time until the battery is drained.
For instance, if you have 4a of loads pulling from the battery, while you are supplying 1a from the solar panel, then the effective drain on the battery is only 3a instead of 4a so it'll take a little longer before the battery is drained.
The real concern is the battery type. "Cranking" batteries have thin lead plates designed to dump a lot of amperage in a hurry. But that large short amp dump is usually only 5% of the battery's capacity. Take it down 5% and then recharge it immediately, and it will do that for thousands of cycles.
That same battery, taken down to 50% capacity, might only last a couple of hundred cycles (if that) before it's ruined. Take it down to 20% and it might only do it 10 or 20 times (if that) before it's ruined.
Deep cycle batteries, have thick lead plates designed not to dump a whole lot in a short time, but to dump less over a longer time (though they can still dump a respectable amount of power in a short time). That sort of battery can be taken down to 50% (or some, to 20%) for thousands of cycles.
I personally, am never in favor of depending on the cranking battery to supply aux loads and then (hopefully) have it still start the vehicle. It might - but there is an equal chance it won't, and that's bad news out in the boonies.
Having an aux battery for aux loads is just about the only way to be sure the cranking battery will be up to the task when needed.
Current: 76 E-250, bubble-top, self-contained|couple of old Yamaha enduros
Previous wheelers: 41 Willys|78 FJ40|78 Bronco|84 Bronco|74 Ramcharger|78 Ramcharger|79 D150 PowerWagon|77 D100|79 D400 dually, converted to 4WD, utility bed, 10' Lance|75 Westy|69 Scout, RHD|bunch of others|bunch of bikes|couple of boats|couple of motorhomes|blah blah|so what|not my idea|just doin' what I'm told|wank wank|this space for rent|candy is dandy|but liquor is quicker