The Toto toilets that use an adapter which would move it back 2" would not work there.
Vespin
Carlyle,
Soirée
Guinevere
The tank would be buried in the wall.
Many plumbers will install at 12.5" in case the homeowner surprises us with wainscoting or tile on the back wall.
Since you have wood floors, you could move the rough-in.
What the plumber did was normal.
Toilets vary in length and how much space is left behind.
He was trying to keep your options open.
Toto Vespin II CST474CEFG with SS114 Softclose seat.
This bowl was installed on a 13-1/2" rough-in using the 14" Unifit adapter.
The water shutoff can be as close as 5-1/2" to the left of center, unless it's higher off the floor, and then it can be even closer to center.
This shutoff had been replaced with a new 1/4 turn valve with brass nipple through the wall.
Installation was by James Love of Love Plumbing & Remodel 206-949-5683
In some of the older Seattle homes, the old toilets had been wall mounted tank toilets.
Those typically are 14" rough-in and need a flange repair to use standard closet bolt connections at the flange.
Everything is on the truck for that.
The Vespin comes with a standard 12" adapter or you can order a 10" or 14" adapter depending on your rough-in distance.