Yes, these are all good points. One of the main purposes of an arranger keyboard is to use the full auto-accompaniment backing styles, but you certainly don't have to. So you might ask, why buy an arranger? And the answer would be to get a large number of high-quality sounds that can be split along the keyboard and layered. But it also depends on if you at least use the backing drums of the styles, like I do.
I say this because, if you do not want ANY automatic background at all, then an arranger may be overkill. If your budget includes a Tyros 5/76, then you can look into the various synthesizers out there, from Yamaha and other manufacturers. Many of them allow splitting the keyboard and layering the sounds, like an arranger, but do not have the elaborate styles that an arranger has. In fact, there is another recent thread on this board discussing the differences, pros, and cons of arrangers versus synthesizers -- you may want to check that out. Some synthesizers do have backing drum tracks, as well, but may not have as much flexibility over those tracks. I was recently reading some information on the Roland Jupiter-X. I don't have the details, but it seems to have a dedicated drum track, and may be worth looking into.
When I bought my PSR-E433, I was also considering a Yamaha MM6 synth, which was being discontinued at the time and was not much more expensive. It did have built in drum tracks, but the reason that I did not buy it was because, as far as I could tell, when using these drum tracks in conjunction with storage memory patches (the equivalent of registrations on an arranger), the memory would also store a particular drum track at a particular tempo, which I did not want. I wanted to be able to choose a particular drum pattern and tempo for a song, and then freely be able to change patches/registrations to get different instrumentation throughout the song without changing the drum pattern and tempo. It is possible that the MM6 had a "freeze" function that I missed, but I did not see it at the time.
So, even though I do not use full auto-accompaniment, I bought what would be considered an arranger (though a lower-end one) because I still wanted background drums, as well as the ability to split the keyboard and layer sounds. It cost $250 US at the time, and there was no way you'd get a new synth with those features for that price.
But for the price of even a used Tyros 5/76, you have plenty of synthesizer options that may be more suited to what you want to do. You just want to be sure of their capabilities if you do want at least backing drums.
Learning chords and chord symbols is definitely a good suggestion for an arranger, or when playing any keyboard, as well. It certainly makes learning new songs easier, whether you use an arranger's auto-accompaniment or whether you play your own left-hand parts. But of course, some people would say it is not as "disciplined" as playing a complete piece of music, with right and left hand parts provided like a Classical piece, as written.
As for an arranger's auto-accompaniment playing the exact bass notes of a particular piece when using one of the auto-accompaniment styles? Yeah, that's not going to happen! The backing styles of an arranger are designed to play a full, orchestral pattern that repeats every measure or so. They are designed to sound good and musically correct when playing a particular chord. But there is no way that a generic background style (such as "rock" or "swing") will know every bass note to a particular song. However, song-specific styles are often available, and I'm sure that these get much closer for the particular song that they are designed for, but I would also guess that, since they are based on repeating patterns as well, they also will not always be 100% true to the original recording of the song. Most arrangers also have a built-in sequencer for recording your own entire songs, so you could actually set one of these recordings up ahead of time, and pre-record your bass line, and then play along with that recording when you want to play that song. But this would involve a lot of prep-work to build a library of recordings for each song you want to play.
It really all comes down to exactly how you want to use the keyboard and the type of music that you want to play.