TL;DR warning. Sharpening is a deep and broad subject, with a lot of opinion and personal preference interspersed with the facts and science so be prepared to have to make your own mind up, i.e. choose your reality and stick with it!
I don't think I missed an explanation as to why he chose to put that bevel beyond personal preference.
Paul Sellers does specify in other videos that he thinks it produces a stronger edge, and also that the convexity allows the chisel — when used freehand in a bevel-down configuration — to glide into and out of a curving cut much more easily than if ground flat, which I can confirm from personal use (my chisel bevels have always tended to look like his, which I used to think was a failing but now embrace as a positive benefit).
The tendency towards forming a slight convexity is a natural consequence of the 'geometry' of human sharpening, which Sellers also explains in a couple of his videos. As your arms extend from closer to your body outwards to the end of the stone the presentation angle naturally gets slightly shallower, unless you're able to compensate for it with an almost robotic precision (usually only achieved with long experience, literally years of practice in many cases) or via the use of a honing guide. Accepting that a curved bevel isn't a bad thing, that it doesn't in any way form a poorer edge (as old books often state outright!) you can just exaggerate the motion somewhat and then you achieve convex bevels in the style of Paul Sellers.
Re. the edge being stronger, although I use a convex bevel myself on any chisel I have re-ground completely I have to say I think this is irrelevant. It is very likely true, but it doesn't actually matter in practice. Here's why: the bevel style that's usually criticised for being the weakest — concave grind with a very narrow honed edge — is almost never known to fail in normal use. I have read of only one or two cases where the edge crumpled and that was when used in tough hardwoods. But thousands upon thousands of woodworkers prepare their chisels this way and obviously don't experience failures, so that should be sufficient evidence that it's strong enough for most users in most applications.
Note: the last point is directly tied to honing angle, which is a separate consideration to the style of the bevel. Regardless of grind style, a steep angle (30° or higher) will always be stronger than a shallower angle (25° or lower) for the same chisel simply because there is a greater thickness of metal behind the cutting edge.
What are some practical reasons to put a convex bevel over maintaining the original hard angle that, in most cases, is already present?
Just to clarify one thing quickly first, the majority of Western woodworkers today do not sharpen and then hone just the one bevel. It's extremely common practice, and has been for many years, to have the honing angle be a little higher, often about 5°, than the sharpening or grinding angle (whether flat or concave if formed on a grinding wheel). This forms a secondary bevel which if very small and as shallow as 1-2° is sometimes referred to as a microbevel; I should stress here that although microbevels should be very very narrow by definition the distinction between the two is often arbitrary, to the point where I think the terms could be considered interchangeable as far as common usage goes.
If we just take it that you have a new chisel with the factory grind on it (usually 25°) and if the metal of the chisel, the sharpening media used and the skill and patience of the user allow you can just sharpen and polish that bevel and the chisel will work well. A well-formed 25° bevel has extremely good cutting performance, but is not suitable for all chisels for all uses. A paring chisel can be sharpened at 20° (sometimes even a little shallower than this) to give superior slicing, bench chisels are commonly done at 25-30° and you can go up as high as 45°, although this is best suited for tough jobs like chopping out deep mortises and general work in very hard woods.
Or perhaps even making a concave bevel?
A concave grind is actually not uncommon, also referred to as hollow ground particularly in knife circles. It's a natural consequence of sharpening a bevel on a rotating grindstone, whether very old-school and cranked by hand, on a bench grinder or on one of the high-end systems such as the Tormek. Whatever the radius of the grinding wheel is this radius will be ground into the chisel bevel.
I feel this question could apply to plane irons as well.
Edge geometry is much less relevant to most plane irons as they present their backs to the work (usually dead flat) and not the bevel, as most planes today are bevel-down planes with a cap iron or chipbreaker clamped to the flat back of the blade to curl or 'break' shavings.
There is some slight relevance to bevel-up planes — single-iron planes, as is common with block planes — but such a tiny portion of the bevel interacts with the wood (the shavings only contact the first 0.5mm / 0.02", if that) that it is really only that portion of the blade that matters and this is almost always flat effectively.
Here are the most common bevel profiles seen on Western chisels:
All of these are in use by someone and although there are specific advantages to some of them (even if only in shortening the time it takes to sharpen) they all can produce acceptable cutting performance. It is the honing angle and the smoothness of the metal right at the edge that are the two primary factors in how sharp a cutting edge actually is, not the bevel profile.
