First's day tickets in the rural South West aren't particularly good value. A day ticket for Somerset is £13 (or £12 on the app), and a day ticket for their Dorset network is also £13 (and that doesn't even cover much of the county).
Contrast that with equivalent tickets covering other rural counties in the region. The Stagecoach West Explorer covers all of their buses in Gloucestershire (and beyond) for £7.50/£7.30, the Wiltshire Day Rover covers all operators in Wiltshire for £8.50, and Stagecoach charge £9.10 for an Explorer in Devon (or for £9.60 you can get a ticket covering all the operators). First's day ticket for Cornwall was very expensive, but the new multi-operator day ticket is £9 which is more in line with the rest of the West Country. Compared to these prices, the fares in Dorset and Somerset are noticeable outliers.
There may be an element of "tourist tax" pushing up the price in Dorset, similar to what you find in the Lake District or on the Isle of Wight. But I don't think that justification works for Somerset, a county which sees much less tourism (outwith Minehead anyway).