+1 to what mykeal states . . . .
In Michigan, you do not need a LTP to purchase a black powder handgun . . . the LTP is basically the "registration" of the handgun which is required and an attempt to screen the buyer in regards running background check and preventing those with felony convictions, domestic abuse issues, warrants, etc. from purchasing a handgun. At the time you pull the LTP, you must furnish your driver's license or state ID which is "run" prior to the permit being issued. Whether a person agrees with it or not, I view it as the state's attempt to do the same thing as when you fill out the FFL forms - and I know of several cases where the LTP process has kept convicted felons from purchasing a handgun . . . at least legally.
I have to deal with the sheriff's department in my county when I purchase a handgun in Michigan. In the past, I have discussed the registration of a BP handgun - necessary or not - and have been told "no". One of the reasons behind the LTP/registration is so that if the registered handgun is stolen, or if a handgun is recovered . . . it can be traced to the owner. In the case of it being stolen/recovered - it can be returned to the owner. (unless used in a crime and held for evidence). For the purposes of the possibility of a BP handgun ever being stolen/recovered - I believe that they can be registered if you want to - this may depend upon the authority issuing the LTP permits. In the past, I have registered antique handguns that are not required to be purchased when I was going to sell them through a FFL dealer on consignment just so there was a paper trail. How the FFL dealer handled them after I transferred them to him was up to his discretion. The sheriff's department never questioned why I wanted them registered as they view the registration as a means of locating the owner in the event of theft/recovery and they were very helpful in informing me what was and what wasn't required.
To the OP . . . nope, it doesn't make sense but then a lot of the laws don't. Laws are made by politicians . . . nobody ever said that they "make sense". As far as being 18 and being able to purchase a BP handgun but not a cartridge handgun . . . I know a whole lot of 18 (or under 21 years old) who aren't mature enough to possess a cartridge handgun . . . but then I also know a whole lot of folks who are older that aren't mature enough as well. At the same time, I find it a little mind boggling that we take 18 year olds into the service, teach them how to operate and fire everything from handguns to missiles . . . ask them to sacrifice their lives if necessary to protect our freedom and rights . . . and then after they are out of the service, the same ones who appropriate funds for the services feel it is their "duty" to restrict them as civilians who need to be "protected from themselves". It's easier to restrict rights than to address the real problems . . . mental health, parents being parents and teaching their kids responsibility, morals and the considerration of others.
Who knows how all of this will sift out when Washington gets done "working their magic". I have a feeling that at some point, BP will be included - after all - you have to keep such things out of the hands of the criminals and we all know they will abide by the law. If you want to take that last statement and fertilize your flowers with it . . . be my guest.