I think it's a very good question, and I mostly agree that for all practical intents and purposes, a good turnbolt is BETTER than a good semi (those practical uses being hunting mostly), due to:
1. Reliability (both general feeding reliability and positive extraction)
2. Lower sight line (better for close-in shots)
3. Lighter weight
4. Easier to shoot from a benchrest for sighting in
5. (very marginal advantage) More "politically correct" looking which could matter to some in some circumstances
Did I mention
reliability, reliability, reliability?
But having said that, I do likes my semis for that theoretical, ain't-never-really-gonna-happen STHF scenario, and perhaps more importantly as a practical matter, that theoretical and could-possibly-happen, 2nd-rapid-follow-up-shot-on-game needed. So I'm willing to take the weight trade-off, and take on the reliability issue, which can be solved with proper mags, well-designed, well-assembled gun, proper tuning, consistent shooting hold, and
consistent ammo.
Now, since (a) I want to cover my contingency bases described that the semi-auto fulfills, and (b) I want to get really really good with JUST ONE rifle, I have thus made my go-to rifle for 98% of hunting & self-defense uses the same one, an AR10 type in .260 rem.
Having said the original statement about a turnbolt being more practical, which it is really (not to mention a lever or pump is as well), there ARE a couple of additional specific advantages to the semi above and beyond capacity/follow-up shots/not moving head between shots, some of which have been mentioned but one of which has not yet been mentioned.
Mentioned was the softer recoil. Not mentioned well the compatibility of most semis (EBR types anyhow), for use with a good single point sling, which I actually find quite useful for stalking/ "still-hunting". Using the single point, or a 3-point for that matter, allows a good way to hold the rifle at the low ready, for hours, without fatigueing as you would do holding up all the weight of a sporter rifle with your arms, since it would only have a carry strap on it, not a sling, then allow you to raise and fire quickly when game is spotted. Since I prefer the stalking/still-hunting method of hunting over an ambush /tree stand setup (which just ends up with me asleep), this is an important point to me.
Now the day that Remington puts a ring on the rear of the receiver of a 700 so that I can attach a single point to it and go stalk, then I'll change my tune, but until then, this is a real *practical* advantage to the EBR style semi-auto - for HUNTING! IMO.