Personally I do not buy into the fact you can run better off a Tri bike.
I have raced Triathlon’s at all levels, Local, National, International in both Elite and AG for 38 years and raced on both Tri bikes and Road bike with clip on’s, also in training I use both, I run the same pace v heart rate with the same overall time’s
Look at the times the ITU athletes run off the bike, would they be faster off a Tri bike, I seriously doubt it.

I would recommend a Road bike and Tri Bike, if I could only have one it would be aero Road bike with clip on’s.
I use my Road bike for
Easy recovery rides, (feel a bit silly at 15mph on the Tri bike).
Group rides
Rides in which I take in the scenery
Exploring new routes.