My question is, can't I simply switch a 5.1 system to stereo mode so it just plays 2.1 FL FR and Sub?
I see no reason you can't. Many of us, myself included, prefer to listen to the source in the format in which it was recorded. Granted, there is really no subwoofer track in a stereo recording but some of us find this "enhancement" doesn't detract from the recording engineers original intent.
Conversely, HT systems offer a means in which it can "stretch" a two channel source and spread it over all available channels. It kerfutzes with the signal and sends "something" to each speaker. Some people love this. Some abhor it. I fall among the latter.
Is this somehow lower quality than a dedicated 2.0 stereo amp?
No. A quality system is a quality system. Granted, with a limited budget, you can get more bang for your buck with two speakers as opposed to five, but all else being equal, good stuff is good stuff.
My recommendation? Since you seem to care about music (and that's a good ting, IMNS?HO) when selecting speakers, bring a two channel CD (or whatever) and listen to just those two speakers without a subwoofer. That way, you can hear exactly what you're buying. An action movie with a lot of boom, bang, and gunshots coming from all around can sound "impressive" on almost any multi-channel system but to sound good on music using only two channels can be quite challenging. A subwoofer will only extend the system's response downward and may affect your judgment when making a decision.
IF a system sounds good for two channel music, you can bet yer bippy it'll do fine with HT. The opposite isn't always true.
Happy hunting.