A sphere small enough to just contain two stars, Sol and Alpha Centauri, would still have a surface area of 60 square light-years. So even that’s going to be difficult, if potentially doable given Trek-level tech and ranges.
Punch that up to 60-70 star systems (even assuming they happen to be bunched up next to each other instead of, as would be more likely, sprinkled across a much larger space with plenty of nonmember or uninhabited stars filling out the spaces between them), and a sphere encompassing 60-70 stars separated by about a parsec each would have a surface area of 830 square light-years.
A sphere large enough to contain the actual nearest 60 stars to Sol would, apparently, have a surface area of 3,100 square light-years.
It may not be the Federation at its height, but it’s kind of a lot.