My tenon saw is sharpened like the first saw you mentioned: relaxed for the first inch and then aggressive. I use it for everything and wouldn’t bother having a different saw for different woods. This saw is 13 tpi. For my style of work, what is most important is set and uniformity. By uniformity, I mean giving a clean cut line without any jaggedness in the cut. By jaggedness, I don’t mean blowing out fibers during a cross cut. On some saws, depending upon the sharpening, if you rip (like cutting a dovetail) and examine the cut, it might swerve to one side or the other if the set isn’t even and / or it might show jaggedness along the ripped kerf…little steps on either side of the kerf. That is what I am talking about. I keep my set very small, small enough that I may sometimes be at the limit of binding and will then lubricate the plate. The net result of all of this is a saw with an aggressive filing, but which leaves a kerf like a dovetail saw even though it is 13 tpi. My fancy LN dovetail saw its on the shelf and I probably should sell it. It is too slow for my taste and too short. Meanwhile, this old Disston 14″ tenon saw does all of my work.
So, I would explore using your aggressive sharpening in everything and see if it actually produces a problem that isn’t solved with a good knife line. In some cases, you may need a pair of knife lines, sawing in between.
What reason was given for having a ore relaxed rake in hardwoods?