I think Rick is absolutely right. There is nothing in the regs that prohibits an LSA from being certified for IFR flight.
But
as many of the new LSA planes have glass cockpits, and seem to have all requirements for IFR flight
Ah but they generally don't. Don't make the mistake of thinking that having the equipment in the IFR part of 91.205 is all that's required for an airplane to be certified for flight in the clouds, or that a manufacturer will choose to have IFR added to the kinds of operations permitted under it's type certificate.
Take the DA-20 Katana/Eclipse as an example - there's a fully-certified airplane that's better equipped than many bigger/faster ones, that is not IFR-certified because it does not meet the anti-lightning requirements for IFR certification. (Due to a quirk in the interplay between the certification regs and the operational regs, the DA-20 is permitted fly on an IFR flight plan so long as it stays out of the clouds; that probably applies to properly equipped LSAs also)