The bowsprit on Argyle was two types of mahogany, laminated from three or four strips. It was painted white but there was significant rot on one of the types of mahogany so I chose to replace it.
After doing some research, I decided to replace it with Douglas fir. Found a place in the Pacific Northwest that harvested old growth Douglas fir and had an adequate piece dried out over about a year. Had the new sprit cut like the old one and painted it with Awlgrip. Since it was fir, I definitely wanted to paint it. If it were a solid piece of teak or mahogany, I might have considered leaving it bare, but I would have at least sealed it up, as I do my cap-rail. For a laminated piece, I think painting is the best option for the reasons already pointed out.
I use Cetol Natural Teak for the anchor platform. I chose that because it would be somewhat labor intensive to sand between coats when using varnish. It's not an ideal coating since it's rather soft and tends to scrape off from sails, anchor chain, feet, etc. It doesn't come off quickly, it's not THAT soft, but I do have to re-coat every two-three years or so.
On my caprail, I use Semco teak sealer. Too many things bolted to and through the caprail to mess around with a coating, varnish or Cetol, and too much of it in any case. Pretty happy with Semco. I re-apply 1-2 times per year and it takes me less than an hour each time. When it fades away, it leaves the rail kind of a dull brown, which is better than grey with black streaks that you get with just oil.