I'm no expert in quill writing by master penman. What I can say is that a lot of people seem to be writing with pointed quills by the late 1700's, some are flexible and some are not, depending on how they're cut and who is using them. By 1800 it's obvious that sharp, pointed and flexible pens (whether quill or steel) are desirable.
The early descriptions of steel pens emphasize more than what we today call "flexible" pens. What you often run into, especially when talking about the deficits of early steel pens, is that they are too stiff, they don't have the "softness" of a quill. What they are talking about is more than just how far apart the tines will separate.
If I may be forgiven from quoting my own blog post (
https://thesteelpen.com/2018/05/03/what-is-action-in-a-dip-pen/)
You’ll often read in old descriptions of steel pens comments about a pen’s “action,” as in “An easy action” or “the action of this pen being similar to that of the quill.”
Action is a combination of the flexibility of the tines (to go from thin to thick), their ability to spring back quickly (to go from thick to thin), as well as a softness to the body of the pen itself. In an 1835 ad I have in my article, it mentions that the action of a pen is "compound." This includes "a gentle, yielding backward action immediately above the nib of the pen [what we call the tines], and, second, the 'scissor' action, or spreading open of the points to permit the flow of ink." This last element is what we generally refer to today as the "flexibility" of a nib. But the people who were moving from quills to steel pens were also concerned that the stiffness of a steel pen (nib) is tiring to the hands, and makes it difficult to write smoothly.
Different manufacturers tried different solutions, from the material the pen was made from, to cutting slits across the body of the pen to create a kind of spring effect, to various kinds of holders that added spring.
As for the tips, which was your real question, the ones I've seen from the transition period of 1890's-1820 were all pointed. I've attached a photo of some pens made in Britain c. 1810. If you look at Williamson's letter, it's obviously a pointed pen. Copperplate was a popular style of penmanship from earlier in the 18th-century and it requires a flexible pointed pen.
I'd say the transition from broad pen points to pointed pen points happened before steel pens were made as a commodity, c. 1800 in England, 1806 in the US.
What allowed manufacturing of pointed, steel pens was the industrial revolution. By 1820's, the advances in quality steel, machine tools and precision machining allowed for the development of the practical screw and more precise tooling, and it was in the early 1820's that some mechanics in Birmingham figured out how to use these tools of mass production to make steel pens. (The Mitchell Brothers, Josiah Mason and Gillott are the primary names associated with these innovations).
Interestingly, the broad nib pen wasn't really made into steel until later. The best guess is that the first steel pens with stub points were made around the 1850's. These were a reaction to the slowness it took to write with a pointed, flexible pen. For those customers who just needed to write quickly, and didn't need it to look neat (because they had clerks who would write out "fair" their rapid scribble), the stub was a wonderful invention. These pens were often marketed to those professions which seemed to have this need for rapid writing: "Lawyers Stub," "Judge's Quill," "Chancellor," "Congressional," and then there's the extremely popular Esterbrook 314 called the "Relief" because it is a relief to write with.
It was most likely around this time you also start to see what became known as Engrossing pens. These included sharper, broad nibs, like we would think of for ornamental broad-pen calligraphy. These were used for "Engrossing" which was the term at the time for decorating documents with ornamental writing. At first Engrossing pens were just another pen in the regular line of pens. Eventually, by the 1880's, manufacturers began to make separate lines of "lettering pens" and these came in specific sizes. Earlier Engrossing pens usually were made in fine, medium and broad.
As for when flexible, pointed steel pens took over from flexible, pointed quills, the tipping point seems to be around the early 1840's. I say this because the numbers of pens made began to grow exponentially. Quills were still being sold all through the 19th-century, the transition from one to the other began slowly but increased rapidly and passed a tipping point by 1850.
In Britain, we have numbers mentioned from early. Josiah Mason began in 1829 making about 20 gross pens that year. By 1830 he had made 100 gross pens, and he was the largest producer at that time. To give you an idea of the scale of growth, in 1846 and 1847, 300,000,000 pens were made in all of Britain (using 147 tons of steel). By 1849, Gillott was making 65,000 gross weekly by himself. (487,000,000)
The US didn't begin to get even close until the 1880's. For the first 3/4 of the 19th-century, British pens dominated the US market.
That was probably way more than you are interested in. Unfortunately, I don't know when broad quills were replaced by pointed quills. I suspect it varied by country. Germany and Russian, with the types of lettering common there, may well have stayed with broad nibs much later than in England or France. I really don't know the traditions there nearly as well as I know the beginnings of the steel pen.
With the steel pen, it was pointed pens which came first. This also makes sense because those who wrote with a pointed quill would have to mend their pen much more often than someone writing with a broad-cut quill. These pointed-quill writers would be much more interested in finding an alternative which did not need constant mending.
Hopefully this was somewhat interesting. If you're not asleep by now, you can obviously check out my site for more history.
https://thesteelpen.com/