Ithaca are the last of of the real values I see these days. You can find a NID 12 in very solid, decent shape for less than $500.00, 16 and 20's for less than a grand. Most decent Sterlingworths are $1,000.00 for a 12 and with that you get a stock with enough drop to make you cry. If you look around you can get a grade 2 NID for about what a Sterlingworth cost.
Flues are even a greater value if you find a later made one. I like the ones from just after WWI until just before the NIDs came out. Some of the engraving is just as nice as the later NID's with wood that is often even better. Been looking at 20 Grade 1 or 1 1/2 as I call them for a few months. If it had 2 3/4" instead of 2 1/2" chambers and be one of the very thin actions which I am afraid of cracking, it would already be at home. But then again, I guess one more gun would fit right in, and prices are going up all the time, and it does swing like a charm.
A few years ago I would have completely agreed with your statement, but Ithaca NID values have really rocketed up lately, particularly in the small gauges 16's and 20's. I don't know that there are very many decent ones out there for under a grand anymore, most seem to be in the $1200-$1500 range.
However, the Flues seem to still be a great value, as you say for those post-WWI models just before the NID came out. I too have looked at those and have strongly considered getting a really nice Model 1 16ga, but those 2 9/16th chambers and thin frame worry me too.
Good advice here and a good thread.