A t2fd sans load will be just a folded dipole, and these are noted as rejecting energy at twice their fundamental frequency of operation.
So if you make one say for 80m, it will be poor on 40m, and show peaks and nulls as one goes thru the hf spectrum. What the terminating load in the t2fd does is broadband it, reducing the peakyness of the standard folded dipole. The folded dipole and the t2fd are both very quiet antennas, I had a 10m folded dipole fed with twin lead and a balun, it was so quiet sigs just popped in out of nowhere, you could hardly hear any band noise but keep in mind that band noise in a quiet location on 10m is very low to begin with.
The t2fd may be more quiet as the load transforms some rf into heat and reduces the composite noise plus desired rf signal levels, comparing wire length for wire length. Speaking of wire length, the more wire you have up, the more rf it picks up from a passing wave, simple as that. Compare a dipole for 2m to one for 80m - each having the same "gain" at their frequency of resonance, yet the 2m antenna will not pick up anywhere near the amount of rf that will be available from the 80m antenna. Also, keep in mind that an rx antenna may reradiate 1/4 to 1/3 of all the rf it picks up, and I suspect that this is where linear loading comes into effect as it helps gather up more of that reradiated rf and sends it down the feedline instead of reradiating it back into the air.