Can you fly IFR in an LSA Aircraft?

“You are not allowed to fly IFR in a Light-Sport Aircraft” is a common dismissal from many in aviation.
Is it factual to say that filing and flying by reference only to instruments in a LSA is excluded by regulation? Is it wise to use these aircraft for flight into conditions of reduced visibility?
By 2017, I venture to say almost everyone in aviation knows about Light-Sport Aircraft and the Sport Pilot certificate, but a superficial knowledge can result in an incomplete understanding. A few details might be helpful.
Think about IFR in an LSA this way: Can you fly IFR in a homebuilt aircraft? Can you do so in a Cessna 172?
Does it matter that these two distinct types have not gone through a thorough IFR evaluation by FAA?
If you know IFR can be done in either aircraft type — assuming aircraft and pilot are qualified and current — then why should such flying be prevented in LSA?
The matter might become cloudier if you heard the advice issued by ASTM F37 on this subject to LSA producers.