Personally, I don't believe jacketed bullets have any place in the 44 Special.
Any potential issue with a lead bullet can easily be solved by choosing the right size, alloy, or, on rare occasions, lubricant.

Keep in mind that the original specifications, which are documented repeatedly in period literature (not to mention data from original sample cartridges), call for a .432" - 433" lead bullet.
Also, most commercial cast bullets are way too hard.

Perhaps this is saying too much, but my theory is that jacketed bullets in the .429-430" range were intended to do two things. First, alleviate pressure in hot loads, and second, offset the issues arising as revolver manufacturers started cutting corners with hand fitting.
In particular, they stopped hand lapping barrels and fine tuning the alignment of individual chambers with the bore.
Admittedly, not everyone agrees with my theory.

In any case, depending on the vintage of your revolver, lead bullets are a good way to treat it right.

Jim