Stains do not provide any protection. Stained wood will easily absorb moisture during high humidity periods, which causes swelling. Expelling that moisture during low humidity periods shrinks the wood---that continuing cycle will eventually cause splits/cracks/etc. Stains also are now washable, the surface left after staining is rough and will collect dust, and sunlight will fade any stain without a protective finish.

Finishing wood properly has no left out steps---the procedures have been honed for hundreds of years.

There is an old adage---Do it right, or do it again.

You can get extra additives to tone down the shine---that would be a much better idea.

Some stains also function as wood sealers. Find out from Minwax how much of a sealer their stain is. To be moisture resistant water should bead up on the surface and not penetrate.

The floor stain/sealers I use seal the wood to a certain degree, however I have never left stained trim uncoated. I coat with my waterborne flooring polyurethanes.

Don't know much about Waterlox, tung oil and hardwax oil treatments, but maybe you should reasearch them. Also, maybe just paste wax over the stain? Just brain storming for you here. Interested to hear what others have as advice for you. I could learn something new too.

BTW, there are some very matte (flat) ployurethane coatings available today. Perhaps Minwax makes a compatible satin or matte coating for use over their stain.

It is simply a matter of taste.
Common oak trim will not just crack and split ( in most climates) just because it does not have a poly topcoat. minwax natural has very little color at all and is much like using a linseed oil or tung oil mixed 20% oil to 80% paint thinner so there will be very little pigment to fade if any but it will fade over time to look " dryer" . There are a few drawbacks to skipping a surface building topcoat in how easily the wood will pick up dirt and stains and how smooth it feels to the touch, but if it is sanded well to 220 grit and you keep it clean and dry you are welcome to appreciate your rustic natural look oak and call it "done" . a suggestion; if you like the look of that natural stain, but you wish for more protection, you can make your own finish by using the oil/thinner ratios I mentioned above or try the same ratio with a satin oil poly and thinner. This very well might give you the same dry natural look, with the same effort, while also instilling some of the waterproofing and uv resistant qualities of the modern poly. General finishes makes a poly that works well with this technique but most any will do the trick.
good luck and enjoy!
Reid