if you don’t shift them well, the dogs can wear out pretty quickly. There are typically only 4 dogs on a ring rather than multiple 10’s of synchro cones. Round off those 4 corners and it’s going to start popping out of gear. Dog rings are Easy to replace in a hewland because the trans stick out the back of the car. Not so easy on a front engine rear wheel drive car. I have friends who need new dog rings every 2-3 race weekends (12-15 hours of track time). Think about what it means to drop and rebuild a trans that often... they really aren’t for everyone, even in a race situation.
Dog ring engagement provides significantly faster up shifting as you only have to lift off the gas enough (or brush the throttle with the side of your foot) to unload them a bit and then you move the lever as fast as you humanly can. the faster you shift the less wear you put on the rings. It’s almost like power shifting when going up thru the gears. Left foot braking is quite handy with dog boxes: right foot matches revs independently of the left foot threshold or trail braking you into a corner. I can’t always doing this well when “in heavy traffic,” because my damn feet have done right foot braking for nearly 43 years.
As far as stronger, that usually comes from the use of straight cut gears, but the whine may drive you nuts without ear plugs.
Finally, it could be argued that Synchros provide a bit of unintentional safety factor in the heat of a race. It’s pretty hard to accidentally go from 4th to 1st in a synchro box. The synchros will warn you by giving more resistance trying to overcome the huge speed differential. Also the slightly slower shift gives you a split second to think, “did I just miss 4th and catch 2nd?” Plus, you aren’t really screwed on a missed shift until you let up the clutch pedal. On a dog box, once you’ve slammed it into the wrong gear (remember, you are shifting as fast as you can possibly move the dang lever), you get HOOKED UP, NOW. Grab the wrong gear at really high revs and you may instantly break the rear end loose and/or blow up the motor. There is very little forgiveness.
It’s pretty exciting the first time this happens to you at 85mph going into a corner. My dirty little secret is that I once saw 10,000rpm on a f*cked up down shift because my gearshift platform moved a bit during a race at WG (Al Taylor knows what I’m talking about) . I got a red hat and shiny bauble and the motor survived the abuse (but it bent both camshafts slightly).
Forget the coolness factor and stick with normal synchros.