My guess is that, like everything vinyl, it's a mixed bag, where one aspect of the equation may influence another. First, 45 rpm discs have the potential for better sound than those cut at 33, all things being equal. But mass market do-nut hole discs were usually made as a cheap commodity, with little thought of sonic quality. It was because the criteria for the product was different than a typical 33 rpm disc.
Because the playing surface (relative to a 33rpm disc) is longer for the same amount of recorded time, 45rpm grooves were typically spaced wider, and the level cut 3 to 4 dB hotter than standard 33rpm discs. These factors were dictated by the requirements of professional and commercial use: limited dynamic range (AM stations often used signal compression) and freedom from potential groove skipping. The gear used to play these discs was industrial strength, to include juke box mechanisms and, for the consumer, portables with ceramic cartridges.
Program material was almost always monophonic pop, thus 2 or 3 minutes of music (and often, less) was the maximum that any disc required. That said, a 7" record cut at -3dB level, and with closely spaced grooves, could contain upwards of 6 minutes or more of recorded sound, but then other problems became evident. For more special purposes, a 7 inch record cut at 33rpm at -6 dB could have about 9 minutes of sound. Some record company promo discs were of this type. I once had a promo Jerry Jeff Walker 7" disc that contained a 7 minute song on one side, and two standard songs on the other. I'm thinking it was 45rpm, but to tell you the truth, I don't actually remember. In any case, the level was cut so low that it would not have been playable over the air because surface noise was about as high as the program signal. [As an aside, during the late '60s, some stereo 45rpm 7" discs were marketed, but their levels were also reduced, as I recall.]
Interestingly, linear groove velocity of a 7" 45rpm is higher than that of a 12" 33 rpm record [at the inner groove the 45rpm is 10.2 ips; 8.5 ips for 12" 33rpm disc]. This would seem to suggest that line contact styli would be a good choice. However, coupled with the fact that the grooves were likely cut wider, at a hotter level, and with less dynamic range, the possibility also suggests that a deep stylus geometry could, in fact, reach in to the bottom of the groove (where plastic residue and the usual contaminates settle) and make the sound worse. For a record with limited dynamic range and limited HF response, a line contact styli may not have an intrinsic benefit over an elliptical or conical. Coupled with likely questionable alignment geometry to reduce weighted tracking error in order to minimize tracking distortion (has anyone made an analysis of this, and is there a protractor out there one can use to align 7" records?) ...well, who knows?
Perhaps the best solution to experiment with would be the Ortofon Concorde. You can get everything from a mono microgroove conical stylus to a Gyger line contact. You just plug in the different styli, and compare. Once the arm is initially balanced, you only have to adjust tracking and skating force accordingly. The only down side is that Ortofon products are on the expensive side. That, plus weighted tracking error is fixed, so you can't make any adjustments with the Ortofon.