Many years ago I had a Pearson 35 - Hull #473, for 6 years; and. then a Sabre 42 - Hull 34, for 11 years; and, our J/Boat now, for going on 19 years, .
The principles are the same for a Cal 30 or tricked-out racer -- it's just a question of degree. On the wind, the boat must heel to some extent to move forward. It won't stay flat unless their isn't any wind or velocity. In 7-8 knots of true wind, the apparent wind will get up above 10-12 knots on most boats that can move with the right sails. Then the boat SHOULD heel a bit. It's just a question of balance. OFF THE WIND IS A DIFFERENT STORY.
Flatter is a relative thing. A Mason 42 of old (a relatively heavy, slower than it looks, beauty) wouldn't move into the wind until it was at about 10-12 degrees of heel. Many people found it amazingly "tender". The ultra lights, even with their relatively deep keels and bulb ballasts deep down also need to heel to move.
On our J/Boat, in 10-ish knots of true wind, when you're going 8 knots upwind, you have 14 knots of apparent wind (or so). The boat doesn't sit-up straight. In a seaway, its comfortable (certainly stable), but it's not "flat" and straight-up going to wind. On faster boats, speed and apparent wind affect one another to change the "true" wind references.
The biggest difference is when you crank the boat off from close-hauled to a reach. Then the heel should moderate and the speed should really pick-up. When you're on a beam reach, things do change a lot until the wind gets powered up.
P.S. - We have three working sails: The main, a working jib, and (an about) 2,000 SF asymmetrical spinnaker. I don't count the storm trysail and jib, which I've never had up in "anger". We didn't get a 130% jib because the effective "range" of the sail is so narrow. On the wind, above 7 or 8 knots, the boat moves for our purposes. On my prior boats, we had 150 and 130% headsails plus the working jib (100%) because they needed them to sail in lighter air.