Whether the caboose had a side door had nothing to do with whether it was a Drover’s caboose. Large side doors like in the CB&Q picture above were generally used on cabooses that carried some freight or express, like parcels to be unloaded at a small town depot by a way freight. Drover’s cabooses had a section with coach seats so that 8 or 10 cowboys could ride along with their bosses’ cattle as they were taken to market.
I believe side doors were banned on a state by state basis; some did it early but some much later in the 20th century - if ever. Since cabooses usually stayed on their owners lines, they weren’t subject to the ICC or other regulations that covered cars used in interchange service.
p.s. the B&M caboose model without end platforms etc. pictured above is probably based on a caboose that was converted at some point from an early small boxcar. Easier to cut a door and a few windows into the side than to rebuild it with end platforms and railings and such.