Excellent sounding LPs

I guess it depends on how you define "audiophile."  I'm inclined to define it as meaning the ambience of the recording venue is well-preserved, so that would eliminate most rock recordings, since they are generally close-miked and generally speaking only live recordings have mics for picking up the ambient sounds.

So using that definition, I'd make a rough guess that half of my moderate collection (less than 1000 LPs) are close to audiophile--mostly classical recordings and some jazz and ambient/new age recordings.  Interestingly, many ambient/space music recordings have false ambience added (through artificial reverb) that conveys the illusion of a two-dimensional soundstage.  I'm not sure whether those should count as audiophile, but many sound as realistic as a mix of acoustic and electronic instruments can sound.

Simplified by percentage, a 20-60-20 Bell Curve (great-average-poor) with audiophile quality being in the first group.

It seems to me that you may need to understand what @fa8362 in particular, but others in this thread so far have said as well.  Do you have cartridge choices?  Do you have a couple of different TTs?  If you play mono records, you need to at least have a mono switch on your preamp, but better is a mono cartridge.  Do you know about the Sugar Cube, which is a digital filter that can dramatically reduce noise caused by scratches and such?  There are a lot of things you can do to make a pigs ear into a silk purse when it comes to playing records.  A good record cleaning machine is a good first step.  It is not just seeking perfect records, frankly there are not very many of those anyway.  Far more effective is to learn how to deal with what you've got.

Couldn’t say, but I don’t care about audiophile quality. I care about music. IOW, I don't play music to listen to my system. I play my system to listen to music.

FWIW: most of the upgrading I have done on my analog front end has been motivated by bringing out the best I can of all my old non-audiophile records, especially my classical collection. If all I cared about was fancy-pants boutique audiophile mastering/pressings I would have been done with upgrades a long time ago. The magic lies in the old run of the mill stuff; e.g. all my Philips classical records of the 70s. That stuff was really well recorded and sounds amazing with higher end gear.

It also pays to have an excellent record cleaning system.

Good question. I would say 98%+. And this has not always been true. My previous system which I used to refer to as my "Reference System", probably only 10 - 20 % sounded really good. I referred to it as my "Reference System" because it was so detailed and sensitive to the mastering and ambience of the recording. If anything was off I would hear it. Here is a vastly simplified version of one of the steps that took me from 10% to 98% sounding good. 

I upgraded my headphone system to a 300B high end headphone amp (Woo WA5). I was shocked at the power, warmth, and musicality of the sound. I remember listening to it the first time. Thinking... wow, that sounds great, I have to go listen to my main system to get the full impact and soundstage. I turned on my main system and it sounded terrible... flat, trebly... like missing the midrange... it was sterile and analytical. It was a $70K system that sounded like schiit in comparison to my headphone system. 

That was the end of my reference system. I immediately started building my next system with emphasis on sounding like "the real thing"... not hyper details and bass. I experienced a decade of season tickets to the symphony and lots of listening to individual unamplified instruments and small groups. What I built is incredibly compelling, musical and emotionally involving. Only albums that sound terrible will come across as such. All the details are there... they are just not highlighted and emphasized. The midrange is natural and fully bloomed. 

So, it is critical how you build your system as to the percent of recordings will sound good.