You can't view all mono LPs the same way. A "modern" mono LP pressed this year is a whole different animal than a mono LP pressed in 1954.
So I'll approach the question in the title this way - first from the two different ends of the spectrum to illustrate the easier cases, then fill in the middle which the question can be a little more difficult to answer cleanly due to many factors. (note I own well over 1000 mono LPs, from all eras, many mono / stereo carts, and my answer also comes from hours of trying many combos over the last few years, plus the hours I've spent researching).
1. What percentage of pre-1958 mono LPs justifies a mono cartridge? Answer:
100%. During this era, everything was mono, plus the groove was cut wider (the 1mil groove vs the modern 0.7mil groove, which appeared post-1958 with the onset of Stereo). You can dip your new microline into 1956 groove all day long, hit the mono switch, and music will come forth from your speakers
but you're not getting the best sound possible. End of story.
Note this class not only requires mono, but further benefits from mono with 1mil (25um) conical stylus, which are not as easy to obtain. I utilize the Ortofon CG DI series and Ortofon SPU Mono - both 1 mil (25um) stylus, with the DI series being a true mono, and the SPU Mono being strapped. Realize though these Ortofons are not ideal for most TT's due to their mass / compliance.
2. What percentage of "modern" mono LPs (say post 1970 for ease of illustration) justifies a mono cartridge? Answer: For those with a modest mono collection -
0%. Even for those with more than a modest collection. During this era, it's all a stereo lathe, and use your stereo cartridge (any profile stylus) and a mono switch (or ycables if its all you have) to achieve near everything you're after. Now, I've played modern mono numerous times with good mono carts too, but most of the time I'm trying to convince myself I'm squeezing more detail out with a mono cart........ but for most it'd be hard to justify a mono setup in this case.
OK, now the tougher era, not so cut and dry.
3. What percentage of mono LPs between 1958 and 1970 justifies a mono cartridge? Answer:
Varies - depends on the LP. This one gets a little tricky for a number of reasons - and those with many early 60's mono / stereo pressing know what I'm talking about. I still go back and forth in some instances on what I try, but in others it's clear cut a mono cartridge is better. In some instances, with as much as I've learned on the topic, I'm just taking an educated guess. Here's why.
3.1 First consider, the 1958 cutover to stereo pressings was not an overnight event, and some smaller shops / labels took years to switch from mono to stereo lathes, some into the mid-60's. Then, even with the big labels, all plants did not switch overnight, there will still mono cut LPs coming out into the early 60's for even the big labels in some cases, at the same time producing stereo pressings. So you could be holding a 1962 mono pressing, still cut on a mono lathe, still 1mil groove. Or you could be holding a 1962 mono pressing, but cut on a stereo lathe with the 0.7mil groove. This is where a little knowledge of label and clues to what it is helps.... though it's never fail safe. If in doubt, don't try and play it with a 1mil stylus (which most don't have anyway).
3.2 Next, I still find that the early 60's mono pressings cut on stereo lathes still sound a little better with a mono cartridge than a stereo - all the way until the late 60's early 70's. These LPs were cut / produced at a time where conical cartridges were the mainstream choice, and many of them were tested with a conical cartridge. I've found even if you don't have a 0.7mil mono cartridge, a conical / spherical stereo cartridge with a 0.7m tip (like DL-103, many others) played, and utilizing a mono switch is better than more modern profiles and a mono switch.
Some of the cartridges I own / utilize for this era are things like a DL-102 (true mono conical, 0.7mil tip), DL-103 variants and a mono switch, AT33Mono, and even some elliptical profiles that are 0.7mil / 18um tip profile with good results. There are a number of mono carts on the market today, for instance the Ortofon 2m mono series, that I'd rather use a DL-103 and a mono switch for this era.
Anyway, as always, it depends on both what LP, and of course what you're willing to invest for sometimes small incremental improvements. I did it partly because I was intrigued by it, and enjoyed experimenting and learning hands on.