but if that is not what is going out through the PA speakers to the audience then what is the point?
why wouldn't that sound be going out of the PA? the goal is to get a speaker that of course sounds good to you on stage, so that you can "feel" what you need to and hear yourself, also creating a great stage mix.
sure, if you had a great PA system with tons of monitors with everyone having their own mix, you could just mix your guitar signal through your monitor exactly the way you want. generally this isn't the case.
a typical PA system, supplied or brought by the band, only has 2 monitors and those are usually for the vocalists to hear themselves over all the other instruments, instruments that usually have their own sound source i.e. drums, bass amps, guitar amps, etc. keyboardists and acoustic guitarists usually don't bring their own speaker, and they usually either can't hear themselves well during the gig because they are in the backline of the band trying to hear themselves through the vocalist's monitors at the front of the stage... or they creep their volume up during the gig so they CAN hear themselves, but then are way too loud for the monitor's intended mix.
even with a great sound system and sound guy, monitors are usually EQ'd and used almost solely for the vocals. many sound guys are trained not to put everything in the mix, but many artists these days want to hear a "CD" sound of their band through that monitor. it's usually not feasible though because the goal is for clarity and reducing feedback. many monitor mixes have a 250hz or so roll-off, so any bass frequencies of the vocal mics don't get reinforced. this of course makes any guitar sound thin and bad. no chug chug there for distortion presets.
so bringing your own speaker is the only remedy for that. of course you should work with the sound guy and make sure you aren't too loud for the room or stage and not bleeding into any mics. that's why i prefer the directionality of the RCF speaker i've recently started using.
now, if you supply your band's pa and it's your band, you can mix things however you want. but again, usually the gear used has limited Aux send capabilities and everyone ends up sharing the same mix, so does everyone want a face full of guitar? maybe not. most people can't feel or play their guitar well if their monitor send is mixed like a CD or even a good FOH mix. guitars are typically SO far behind the vocals, brought up only for leads etc. but if you can play like that, that's great for stage volume.
a question for you: if many bass players DI into the FOH anyway, why do bassists bring an amp setup? why not just use the PA system?