Is that necessary to get that particular bullet to ram in straight and/or is it peculiar to a flat tipped plunger?
It's peculiar to a flat tipped plunger. For the most part.
The Accurate Molds 45-190R and 190S, and the Lee 450-200-1R, all have something of a ball end. Depending on how, or to what degree of "secureness" the plunger self centers over the bullet nose, you may be perfectly OK without locking the cylinder.
The totally flat tipped plunger has no way of centering over the chamber, so the the chamber is slightly out of alignment with the plunger, the plunger will be forced hard into the chamber mouth, deforming it more or less, depending on seating pressure, the hardness of the steel, and the degree of misalignment.
A round ball self center very positively with the chamber, and a theoretical plunger with a near hemispherical tip will center very positively with the ball. Thus the plunger is positively centered with the chamber. That's the best of possible scenarios. The Remington under doesn't really have that much positive engagement with the ball, but it's seems to me that it works pretty well leaving the gun on half cock while seating round ball.
There is another issue though, nearly, or just as, important as the plunger tip shape. The Remington design, as beautiful as it is, has a serious flaw. Due to the geometry of the loading lever and link, the link is placing nearly as much force upward (toward the cylinder arbor) as it is backward (toward the back of the chamber, it's roughly a 45 degree angle AT THAT MOMENT WHEN THE PLUNGER ENTERS THE CHAMBER. A conical bullet may fit and center perfectly with the plunger, BUT if the plunger is fairly loose in the frame (mass they tend to be) and the plunger has very little support in the frame because most of it is spanning the gap inside the loading window as the plunger tip first enters the chamber, the the plunger can force the nose of the bullet upward toward the cylinder arbor.
So it is that Yolla and I have both built new, extended length plungers. The extra length means that the plunger is fully supported in the frame as it enters the chamber mouth. The large off-axis force applied to the plunger by the lever link therefore results in very little off-center-drift of the plunger tip, so conicals of any type will seat straighter AND the plunger is physically incapable of touching the chamber mouth (at least when the cylinder is in lockup).
So there are two issues there. One is plunger engagement with the projectile (a flat tipped plunger has none) and the other is the plunger being forced off center by the lever link. They're related, but separate. The "nose" of a round ball is very close to the ball's "drive band" also, whereas a long nosed conical has it's nose much farther away from the front drive band. That means there's more possibility of forcing a long nosed bullet off center during seating IF two things occur at the same time-- The hollow tipped plunger engages securely with the bullet AND the plunger is being forced off center by the lever link.
I've dinged the hell out of all the chambers in a Remington doing that, seating very hard near the chamber mouths, meaning that your load is such a full one that your maximum pressure on the lever occurs with the tip of the plunger right at the chamber mount. Nasty! That's when I decided the gun needs a much longer plunger, with the lever modified to accommodate it. You've seen the photos.
Also further submit that a lot of the chainfires that occur, which we never experience, are facilitated at least in part by dinged chamber mouths. That's never addressed in the manuals.
The Colt "creeping" style loading lever as designed by Root, which Colt later also used on all the 1860 and later percussion revolvers, is vastly superior in that regard, as it places an almost perfectly linear force on the plunger, and the plunger has much more support in the barrel than a Remington plunger has in the frame. So if you want to shoot a lot of conicals and want to keep any required gun modification to a minimum, get an Uberti Colt '60 Army. Or not. The Remington does have it's advantages too. The Colt needs a cap rake at minimum, and you'll almost certainly want to form fit the plunger tip.
Stuff like that. And so it is again that I'll say "we design the bullet for the gun and the gun for the bullet". They had it largely figured out in the 1860s, but I'm still learnin'.