The dirt on a baseball infield extends out to an arc centered on the lip of the pitching rubber (60' 6" from home) and has a radius of 95'. This makes the distance from home to the very edge of the arc 155' 6" and the distance to the edge of the dirt along the foul lines about 127'7". Why was this value of 95' chosen? Why not, say, round it up to 100'? Or make it 90' to be consistent with the basepaths? Or perhaps shrink it to about 70', which is about the minimum size needed to fit all the bases inside? 95' just seems like such an oddly specific number that there must be a reason for it. But searching the internet just gives results explaining what the dimensions are and how to construct a field; I can't find a source that explains why a radius of 95' was chosen.
Like @Joe said in the comments, I could not find the answer, but I believe that the infield arc has a radius of 95 ft. because it makes sense with the timing of the runner so that fielders can make good plays, but it is also a short enough distance (90 ft. base paths) that the runner can still beat out an infield hit. If it was longer, say 100+ feet as you mentioned, then it would be like having to gun a runner at third from the outfield whenever the third baseman had to throw to the first baseman. Also, if the radius was larger, then the base paths would be longer and it would be harder to get hits and XBHs. However, if they were a lot shorter, say the radius was 70 ft. as mentioned in the question, the distance between the bases would be a lot shorter, and routine ground balls would become infield hits for the faster runners. Also, I think that they (the people who created baseball) made the infield arc 95 ft. because they wanted it to be a diamond and not some other random quadrilateral. I believe that the infield arc was also made this distance for base stealers; the catcher could gun them down, but they could still be safe at least (for most) 2/3s of the time.