The process to purchase a suppressor is not that difficult. It consists of five pieces of paper (reducable to three if you do a trust or corporate transfer), a couple of photos, and some signatures.
Even doing fingerprints, I can have a customer out the door, on their way to get some photos in under 30 minutes. After getting photos, they head to the Sheriff's office, and drop off their paperwork. The Sheriff signs it within a day or two, and the customer mails it all to BATFE.
Currently, the longest part of the process is its travelling through the US Postal Service system. I get transfers back in 4-6 weeks. It takes 2-3 days to get to Atlanta. From there, the check is deposited into the bank and the rest of the paperwork is forwarded to Martinsburg, WV, another 2-3 days. Then, the BATFE forwards the fingerprints to the FBI. The BATFE examiners do a quick background check, and once it comes back clear, and the check clears the bank, they affix the stamp, and mail it back to the FFL, another 2-3 days. Add in the weekends, and the paperwork doesn't really sit on an ATF examiner's desk very long. Especially compared to the 5 months and longer transfers that used to be the norm.
If only NFA 34 were amended, allowing FFL's to input the data into a computer and scan in fingerprints. Technology is definitely capable of doing the job. We can do instant checks for Title I guns, and cops can do fairly rapid checks on fingerprints. It would be easy to write a program which stops the transfer if the item is illegal where the person lives. That would also eliminate overbearing CLEO's, who don't feel you should have an item, regardless of the item's legality and your clean record.
But, that's just a dream world.