Someone did two "kitchen table" modifications.
One I could overlook, but, two ?
I see a possible third one. The rear sight blade notch. All the Millets I have ever seen have had square notches. So,we have the baseplate on the grips, an after market rear sight, and (I believe) a modification to the rear sight notch.
The baseplate can only have two possible functions, to protect the bottom of the grip from something, or as a way to add some weight to "adjust" the balance of the gun in the hand. Only the previous owner could tell us just why he did that (or had it done). The actual fit looks pretty good, and that argues against it being a "kitchen table" hack job. Also the Millet rear sight, which again says something against it being a "bubba" job.
I'm going to offer a little different advice. DON"T remove the sideplate. Instead, take a close look around the edges, looking for any scratches or burrs. If it looks good, you can relax a bit.
There is a right way, and several wrong ways to remove and reinstall the sideplate. Its good advice to take it down, check the insides for damage, "bubba" trigger jobs, etc., BUT if you don't know what you are doing (have some training and experience) its better you don't do it. A single slip or doing something wrong can damage the finish, and even the fit. Also, a fumble at the wrong point, with the sideplate off and you have a jumble of parts you have to put back in the frame. And I'm guessing you aren't experienced with that, either.
You say the trigger is "sublime". Original triggers are good, and can be "sublime". And a trigger job done by someone who knew what they are doing is also.
If the gun is working properly (check out the sticky thread for used revolvers as to things to look at), the only reason to remove the sideplate would be if you wanted to, or you were told you had to, and believed it.
One thing to look at, is the forcing cone. The rear end of the barrel where it stick out of the frame. Clean it thoroughly, and under a good light (and maybe a magnifier) look for cracks. There shouldn't be any. If you see something like that, don't shoot it, and have it checked by a professional, one who knows what they are doing with S&W revolvers.
Also, since you have the grips off, look at the strain screw. This is on the front of the gripframe, and puts tension (strain) on the mainspring. The head of the screw ought to be approximately flush with the frame. If it is screwed significantly more in, or out, you might have issues. Some people will adjust the screw as a way of changing the trigger pull, but it can lead to erratic ignition.
If I were you, and assuming the gun checks out good (locks up properly, etc) I'd get a set of Pachmayr grips, which ever style you like best, and shoot it. The rubber grips don't look "pretty", and they aren't to everyone's taste, but for me they work very well, and are better in my hands, for shooting, than the factory wood.
I would also recommend not shooting much of the 125gr JHP ammo. Any other bullet weight is fine. There is a long history of model 19s and too much of the 125gr JHP load having issues (including cracked forcing cones).
Looks like a really nice gun, with some modifications done fairly well. We may not agree on if they were a good idea, but they appear to have been done well, mechanically. That, and the overall finish condition argue that the previous owner wasn't a hackmeister. Not conclusive, of course, but if the gun is working properly, I wouldn't lose any sleep over it.
Enjoy!