On the other hand, if you want to ask if anybody is working a protein sub-unit vaccine, the answer is yes, NIH announced on Dec 28 that Novavax began phase III trials for NVX-CoV2373. (They are actually conducting concurrent trials in the UK and Mexico too.)
According to a story in Science, Novavax uses armyworm moth cells to grow these proteins; the spike protein DNA is transfected to these cells via a baculovirus. The Science article also mentions that Novavax has had some issues with scaling production. As I mentioned in my answer to the related question, in general "manufacturers are challenged to balance the competing goals of speed to market and process optimization". (One can also find more in-depth articles on animal trials and phase 1-2 trials for this vaccine.)
There are also at least two Chinese vaccine candidates that use a protein sub-unit, one in phase III trials (Anhui Zhifei Longcom -- ChiCTR2000040153). This is one is interesting perhaps because it aims to immunize against MERS and the original SARS as well. For the biotech inclined, there is actually a technical paper from a 3rd group (linked to the Swiss biotech ExcellGene) on making SARS-CoV-2 proteins in CHO bioreactors, which is what the aforementioned Chinese group is using as underlying tech, broadly speaking.
And a review linked from that paper discusses the challenges with these protein-sub-unit vaccines in general:
such vaccines also have disadvantages. The spike protein is relatively hard to express, and this is likely to have an effect on production yields and on how many doses can be produced. The RBD is easier to express; however, it is a relatively small protein when expressed alone and, although potent neutralizing antibodies bind to the RBD, it lacks other neutralizing epitopes that are present on the full-length spike. This might render RBD-based vaccines more prone to impact from antigenic drift than vaccines that include the full-length spike protein. Many recombinant protein vaccine candidates against SARS-CoV-2 are currently in preclinical development, and several spike-protein-based and RBD-based vaccines have entered clinical trials [...]
Of further note here, the (Chinese) Longcom vaccine only targets the RBD, while Novavax's targets the whole spike protein.
The most recent review on vaccine candidates I found (Dec 20) mentions that some 13 companies actually have protein sub-unit vaccines in clinical trials, at various stages, with Novavax being the one that has done most testing up to date.