Have you found that this affects regular use and cleaning?
Absolutely.
When I first got into Cowboy Action Shooting I was shooting this Winchester Model 1892, chambered for 44-40. At the time I was shooting ammo loaded with Smokeless powder in it. As I believe I said earlier, the thin brass at the case mouth of 44-40 expands very well to keep blow back into the mechanism to a minimum. Very little fouling was getting past the case in the chamber into the mechanism. I would clean the bore and do a little bit of light cleaning in the exposed parts of the action. I only took it completely apart once, never plan on doing so again. As you say, Mr Browning's design is a pain to take apart, and it is easy to reassemble it with one of the parts in backwards. It's been a long time, so I don't remember now exactly which part that was. I suppose if I took it down often enough I would get more familiar with putting it back together again, but about that time I started shooting 44-40 ammo loaded with Black Powder in an Uberti replica of the Model 1873.
This is a view into the receiver of that Model 1892. The carrier is folded down in this photo, but it should be evident how any fouling that gets past the chamber will be deposited directly into the mechanism. By the way, take note of the 44 W.C.F. marking on the barrel, calling out the cartridge it is chambered for.
Here is a shot inside a different '92, this time with a fresh cartridge riding up the elevator ready for the bolt to shove it into the chamber. Absolutely nothing to keep fouling sneaking past a round in the chamber from getting into the mechanism.
There is only one screw holding the side plates onto the frame of the Model 1873. The carrier, or cartridge elevator resides in the space in front of the side plates.
Remove that one screw and the entire toggle link assembly is exposed. The links pop right out, sometimes when you don't want them too, and this makes the mechanism of the Model 1873 completely accessible for cleaning. Hmmmm, I must have taken this photo of the links in this original 38 W.C.F. Model 1873 before I did any cleaning.
The top of the frame in the area of the carrier of all the Toggle Link rifles; the 1860 Henry, the Winchester Model 1866, and the Winchester Model 1873, is completely open. There is a sliding dust cover on top of the '73, but after working the action once the dust cover stays open. This is a photo of the bolt shoving a fresh cartridge off of the brass cartridge elevator and into the chamber.
This is what the top of the frame looks like with a fresh round in the chamber. The bolt is completely forward, holding the round in battery in the chamber. Yes, at some point somebody did a nasty to the screw at the top of the dust cover.
So from a practical standpoint, I discovered that with the superior expansion of the 44-40 round, plus the way the bolt will block almost all fouling that happens to blow by the expanded case from getting back into the area of the frame where the toggles live, there is almost no reason to take the side plates off and clean the mechanism anyway. When shooting my Uberti replica 1873 I would take the side plates off, remove the toggle links, and clean that area of the frame maybe once a year. There was always hardly any fouling in there anyway, even after a year of CAS matches.
These days my Main Match rifle in CAS is an Uberti replica of the Iron Frame Henry rifle. It is chambered in 44-40, my favorite Black Powder cartridge, and I only shoot it with ammo loaded with Black Powder.
The Henry is more difficult to take down than Model 1873. They both share the same basic toggle link design, but the side plates on a Henry are dove tailed into the frame at their front and rear. To take down a Henry, first the lever screw, which runs through the side plates, must be removed. Then the side plates need to be driven down,usually by striking them at the top with a soft faced hammer. And the front and rear edges of the side plates are razor sharp where they fit into the frame, so great care has to be exercised when removing them. I just went through my hard drive looking for any photos of my Henry with the side plates off, and I do not have one. Suffice it to say, I seldom take the side plates off my Henry to clean it.
This is the view down into the mortise where the carrier resides in my Henry. The carrier is in the lower position, and the bolt has been withdrawn. A round is on the carrier, ready to rise and be fed into the chamber. Notice the vertical wall of the frame behind the carrier. This is the same as in a '66 or '73. The hole in the wall is where the bolt will poke through to shove a cartridge into the chamber. This is a good illustration of why any fouling that blows by a cartridge in the chamber will be pretty much completely prevented from blowing back into the area where the toggle links are.
One more photo showing the lever of my Henry in the forward position having raised the carrier. The side plates where the toggle links reside is clearly behind the vertical wall in the frame
So, to get back to the original question, yes, the layout of the frame on any of the Toggle Link rifles; the 1860 Henry, the Model 1866, and the Model 1873, tends to prevent Black Powder fouling from getting into the area where the bulk of the mechanism resides. The fact that the side plates on the '73 are easily removable, does not change that. I cannot remember the last time I took the side plates off of my Henry to clean in there. Next time I do, I will take some photos.