Which spectrum is more desirable ultimately comes down to two factors quality and quanity, but beyond that Yoda has an interesting point. There's no test evidence one way or the other to show (that I know of) whether ambient heat is a reasonable analog to directional or somewhat directional radiant heat. It's reasonable to suspect plants are optimized for a certain degree of both ambient heat and solar IR.
It's been documented enough IMO to suggest that spectrum plays a small part in the equation but when considering the efficiency gains -vs- yield gains, is it hampered to some degree by a loss of directional IR? I don't know.
If there was something to it, it could be possible to improve yield density with some full spectrum IR added, but additional energy use could negate any possible benefit in terms of yield per watt. If this is all true then HPS bulbs do provide free IR. Turning up the ambient temperature might offset this effect to some degree, but it's not a direct analog.
Take with a grain of salt. Beyond GPW there is GPParW. It's rare to see HPS growers hitting +1.5 GPW and LEDers getting ever closer to 2. That's efficiency. When yield is broken down further, compared to only the PAR emission, the impressive results with both types of light might be about 3.5, even 4 GPPW in some cases with peeps who know their shit. More common results using both types of light will be in the 2-3 GPPW range. This is based on various anecdotal postings I've read over the years and isn't well tested science, but I don't get the idea a PAR watt's worth of HPS light vs a PAR watts worth of LED light are much different in terms of yield and quality.
LED DIYers today should be looking at 55-65% efficiency at the cob/board/strip and using 1/3 to almost 1/2 less wattage for the same results. An additional benefit if that's not attractive enough is the expectation of years without any part cost or labor and almost no intensity loss across the same period.
Over the next few years I predict we'll see the decline of the bulb in all applications. It will be difficult to argue HPS is better when nobody is using it anymore.