And yet I cannot find the term "airplane" or equivalent anywhere in your post #68.

I was addressing 'your' physics.

Well, I was posting on "Flyer Talk" in a thread about the speeds of passenger jets. What do you think was the context of my post and how many people do you think thought I was commenting about the speed of sound in materials other than the atmosphere?

What matters is capacity per day, not capacity per flight. Shorter flight times mean more capacity per day. This is more noticeable on long routes, where ground turnaround times (not affected by aircraft speed) are a smaller fraction of the total, but it has to be taken into account in any case.

Fuel costs and other factors still matter, of course, but any calculation has to begin with the right concepts.

Another way to increase capacity at Mach 5.5 speeds, that's about 3000mph. Most TPAC routes would probably be 2.5-3 hours in length. At these stage lengths, you can consider putting in standing room only seats so you can fit more people in. I spend more time than that standing in line at Disneyland than that in one day. You definitely will no longer need to have first class suites and you can put in a couple slimline coach seats to serve as "First Class". Also at these stage lengths, you can probably get away with not serving meals and have just basic drinks service, further reducing weight as there would be no need for ovens. You also save on lav tanks as you only need enough to support a 3 hour flight max. If an airline can get me to SYD from LAX in 150 minutes, they can give Ryanair service and I'll still pay for that speed!

Also, if it becomes cheap enough to fly those routes, then pax can go TPAC for shorter trips, thus carrying fewer bags, further reducing payload.

Very few posts on FT concern themselves about airplanes. And yes while the atmosphere on Earth is gaseous, you did not even address an atmosphere in "It is actually temperature, not altitude. Sound moves slower as the temperature decreases".

But more seriously, you are as wrong as you are right - if you recall the square of the speed of sound in an ideal gas proportional to pressure over density. And in an adiabatic gas you can rewrite this to depend solely on pressure OR temperature. So the statements are equivalent.

I think colloquially, the argument is that density at constant pressure decreases with the third power of temperature but pressure in the lower atmosphere decreases exponentially with altitude. So the effect over a large range of values is more sensitive to altitude than temperature ... if you accept air as an ideal gas.
But of course for a constant gas mix, the two are not separable.

Achieving hypersonic flight depends a lot on a light aircraft, so it can climb to ultra thin air.
I said the LAPCAT would cruise around 80k ft, but I later found its intended cruising altitude is 100k ft, that means the aircraft has to be very light. So the thought of squeezing more people on such aircraft is nonsensical, there just won't be enough payload capability to do that.

No, capacity for flight is critical because each flight has a unique cost and it's own profit margins. Airlines measure this to audit the profitability of each individual flight and adjust pricing accordingly. This is part of why it's not all a flat rate, or only distance adjusted pricing.