Summation isn’t everything, if the delay that’s added on the bad side is moving the centre one way caused by a dominant reflection , and you add an all pass on the good side so it matches and sums, it’s very possible to push the centre further away, we can only add delay with all pass filters (how much is freq dependant, the higher the all pass the less delay it adds… a second order adds one wavelengths delay) so a very small amount at 1.6khz vs 160hz)
every effect has a side effect whether it’s desired or not is another matter [emoji1360]
So in my midbass example above, you would simply leave the phase-related dips there? Or would it just depend on whether you hear any "bad" side-effects after using allpass filters to fix them?
Obviously, I listen to the system both before and after I make changes. If I hear anything "off" afterwards, I wouldn't leave it in place. However, that hasn't been my experience - at least with my system. I have not yet noticed any "bad" side effects from allpass filters that I've used - but I do get better summation.
In some cases, the dips that are corrected aren't necessarily easily audible via your ears - but that is kind of the reason why we use RTA's to begin with - to identify and correct issues to a point that is just not possible using your ears alone. Otherwise, we wouldn't use an RTA at all - we'd just tune everything by ear.

However, all of those little "imperfections" add up and may be audible in certain situations. As long as they don't cause any audible (non-wanted) side-effects, I see no reason why wouldn't want to get the phase to match between L and R and get as much summation as you can.
I might get abuse for this, but - all-pass filters are not really for amplitude ("RTA") issues. Those dips on the graph above would not really be noticeable in themselves.
All-pass is for coherence, imaging, soundstage. Amplitude dips are a good way to see the problem, but they are not the problem that you are trying to fix. You are trying to keep phase the same L to R, and through a crossover region. This is best done by measuring phase. I struggle with OpenSoundMeter for hitting a target curve, but that is the type of tool (or a more serious/paid for alternative) that is best for setting up all-pass.
I completely understand that you are better off actually measuring phase directly. However, as you stated - those dips are just another way to identify phase issues. Using an RTA to identify phase issues like this may not be as accurate as actually measuring the phase, but why not make the phase match between L and R and get rid of those dips if you can (as long as there are no audible "bad" side effects)? In my case (and probably lots of others), I really don't have the correct equipment to properly measure phase and correct phase 100% - but in cases like this, it's pretty obvious that these dips are phase-induced. I am simply using the tools that I have to identify and fix what issues that I can. If you can use an allpass filter and get the L+R responses to sum better, without any audible side-effects, that seems like a "win" to me.
That is kind of like saying that you shouldn't fix an issue with your car because a mechanic can fix it better/faster with better tools. At the end of the day, if you can fix the summation without any bad "side effects", then why not? Sometimes, you use what you have and do what you can with what you have.
