OMG! Someone used "ATF" and "efficiently administer the NFA law" in the same post. (Sorry...my black humour occasionally surfaces.)
Alexander has made some valid points and done it very well. Another issue that has been pursued in the past is that the Forms 1 and 4, among others, are essentially federal TAX documents and fall outside the purview of local law enforcement. That argument has not yet been accepted by the ATF, but it does get resurrected now and again.
Verifying the trust documents or articles of incorporation on non-individual requests actually takes much longer and has been one of the reasons that the process has yet again bogged down. It was nice to have your Form 1 turned around in 3-4 weeks; that did not last with the increase of corporate and trust applications.
Alexander is also correct about the "artificial roadblock". There are states that simply do not allow possession of any NFA items. Having the CLEO sign-off in 'NFA-friendly' states is a useless waste of time. A NICS check will garner the same results for ATF that it will for the CLEO. In less gun-friendly states like the People's Democratic Republic of Maryland, one cannot even transfer a legally owned handgun to another individual without going to a State Police barracks, filling out some paperwork and waiting at least a week while it is processed. The states can add to the law, but not take away or ignore parts of it. So if the CLEO thinks there is sufficient reason to restrict ownership of NFA itmes, he/she should take it to the legislature and have the STATE law changed. As it stands, it allows the CLEO a measure of power that the constitution never meant him/her to have. (Of course, if you can find a local judge or justice of the peace to sign off, you can ignore the sheriff or chief of police. Now THAT is what I call a loophole.)
My local guy is Larry Dever, Sheriff of Cochise County. We have bigger issues down here on the Arizona border than whether I can own NFA firerams. Since I know Larry pretty well, I just carry my paperwork to a local function and catch him there. Otherwise, driving down to the county seat to drop it off is a big PITA in addition to being unneccesary. Once I have an approved Form 1 or 4, it should not be hard to verify my eligibility for further acquisitions.