No, no, no --- Not even close. The point to NORMAL (let's get that out of the way - It's not "lower" - It's "normal") recording levels is to not overdrive the input chain. It has nothing at all to do with the mix buss. The fact that it give you a little more (though rarely ever enough) headroom at the mix buss is is simply how the system is designed. Although that design works much better with converters calibrated to -20 (and I "pretend" they're at -24, as I'm a complete whore for headroom). You get one chance to digitize an analog signal. Once it's captured, all the rules change and there's no going back.And I think you're missing the point of the lower signal levels. As MSE indicated, it's primarily to avoid overloading the mix bus (your final 2-track output).
If your converters are calibrated to -14dBFS (seems a little high, but I suppose there are still some out there that haven't read the memo), and your front end is spec'd to line level (as basically every single piece of gear in the world is), then a "normal" level would be -14dBFS.
Point: Some (SOME) pieces of gear out there have a good a mount of usable headroom and sound fine above line level.
Counterpoint: I've never actually heard a piece that sounds *better* above line level - I should correct that -- It's very rare, but it does happen, that certain pieces change in "flavor" -- Amek, Neve, API make a few a pieces like that - But again, you'd need your converters way down at -24 or -20 to take advantage of it - and the "flavor" is a personal preference to some - Nothing illegal, but worth noting.
Counter-counterpoint: I've heard soooo many pieces that sound better below line level...
Back to the point on compression on the input chain -- Ideally, you'd want to set your preamp level first and allow the compressor to reduce the gain without adding it back. Digital gain will be cleaner - and you'll not fall into the trap of adding additional gain at the preamp which will take it out of it's nominal "sweet spot."
NORMAL levels - Lower noise, lower distortion, better signal-to-noise ratio, better focus, higher clarity, etc., etc., etc., yada, yada, on and on. There is nothing "normal" about recording levels up short of clipping. No matter what the manual or the marketing company might say.