I agree. I used to do a lot of restoration work and came across this type of finish. Whatever was under the polish in items I repaired could have been left its natural colour to start with, or alternatively the bare wood could have received either/or/or both dye and stain followed by clear and/or tinted polish.
Here, I suspect you think along similar lines to me in that its probable or possible the only thing that's been applied is a tinted or toned polish over bare wood, and it's now flaking off; somebody may have had a bit of a go at adding some more polish to cover the bare wood, but that's hard to say. It looks to be a decent but not spectacular piece of furniture, probably from the period you indicate, and not especially valuable. Still, it could be made to look decent along the lines you suggest with stripping and refinishing: refinishing from bare wood would be an opportunity to do a variety of things, e.g., colour up or not, and apply a finish of choice e.g., shellac, varnish, lacquer, or even something like one of the Osmo products, etc. Hardware, something reasonably matching, or even a really good match could probably be scrounged up inexpensively from somewhere - ebay, salvage yards, auctions, junk shops, etc. And if a whole piece of furniture has to be bought just to get three or four bits of hardware, well, maybe that could also a be a source for some salvageable and usable material too, ha, ha. Slainte.