For 10 years or so, all Honda owners' manuals have stated: "If Honda MTF is not available, you may use any SAE 10W-30 or 10W-40 viscosity motor oil with the API Certification seal that says 'For Gasoline Engines' as a temporary replacement. However, (the manual goes on to say) motor oil does not contain the proper additives, and continued use can cause stiffer shifting. Replace as soon as convenient." (Emphasis added.) (Quoted from p.325 of the current Accord manual.)
Note further, the Accord manual does not say regular motor oil will eventually cause stiffer shifting, only that it might. In this regard, for decades before Honda started selling its own MTF product, Honda transmissions were filled with 10W-30 weight motor oil. Indeed, even now Honda MTF is, in fact, conventional "motor" oil with various additives. (You can find an analysis of Honda MTF on bobistheoilguy.com.)
Current owners' manuals go on to state: "The transmission should be drained and refilled with new fluid according to the maintenance minder." This, too, is significant because Honda doesn't require replacement of the substitute oil "as soon as possible," nor is there any admonition about additional wear, etc.
Consequently, several years ago, after reading the above quoted language for years, I decided to experiment using Mobil 1 synthetic motor oil in a Civic Si (EP3) transmission to see if shifting would improve using a synthetic oil (particularly in cold weather), and whether synthetic motor oil would, in fact, deteriorate over time or miles driven. I considered using Amsoil synthetic Manual Sychronmesh Transmission Fluid, but that wouldn't have told me what I wanted to know WRT the use of synthetic motor oil, and Amsoil's product, while excellent, costs about three times as much per quart as Mobil 1.
Cutting to the chase, Mobil 1 (5W-30 -- the same viscosity as Amsoil's product) works great. I still own the Si, it's gone over 50k miles with M1 as its sole MTF, and it shifts like butter, hot or cold.
Finally, for the sake of clarity, let me add I am not "recommending" M1 as a substitute for Honda's MTF. I am simply pointing out there are alternatives, and in my experience, M1 works well.