Some thoughts

First of all, what gauge?Let me assume HO. There is a difference between roadbed and benchwork. Track lays on roadbed. Which can be cork or foam. I made mine out of posterboard, Cut into strips. Top layer just wider than the ties. 1-3/8" to 1-1/2". An underlayer 2" to 2 1/4". That was my cheap way. As for what your picture aludes to is benchwork. That can be as narrow or wide as you like. A club that used laminated wood/lattice strips made it just a smidgen wider than the ties. Another club used plywood/which looks like what you have shown above made it 3" so as to have room to attach scenery. The laminate had the scenery attached to the side. Is this clear?  Morgan

A 2.5 ratio

I use in N scale a 2.5 ratio  width of the track for simple track; this mean my ME track is 17mm width, roadbed is 42mm width 

A two track is 17 + 18 ( space between ties of two parallel track) + 17  X  2.5 = 79mm

This is broader than track but just enough to glue scenery support along the roadbed; I increase this a bit due of cutting necessity but this remain for a few mm in the 2.5 ratio; I use it since 40 years with excellent result and ease to connect scenery or scenery support to the roadbed.

Sorry. I model in HO

And as Morgan said, I am referring to the benchwork.  The width of the track and ties is 1 1/8 inches.  Someone at my railroad club suggested just 1/8 on each side, which seems a bit small.  Not much room for ballast.  Maybe 1/4 inch on each side?  Or just measure 1 1/2 inches and start cutting.

@gary YurgilThe 2.5 ratio

I think you can use it in HO too; make a calcul with it and see if it's usuable for your needs.

what's the downside?

Gary, what's the downside if you make it too big? And what's the downside if you make it too small?

I suspect if you answer those questions for yourself you might decide that too big is better than too small, as you can always come back around with a jig saw and trim some off if you find you have more than you need.

 "How wide should the track

It depends on the topography of your route. If the track has steep slopes on the side then your sub roadbed needs to be narrow enough to allow the scenery to slope down. If it's a less steep slope you can make the sub roadbed  a bit wider. I'd draw a cross section of a few spots then vary the sub roadbed width to best fit the slopes....DaveB

Roadbed profile

The profile would/could be very different based on the era and class of railway. Below is a CPR mainline standard and the ballast slope is about five and a half feet beyond the outer rail. Many were only 5’ (11/16” in HO scale).

From your post it seems as though you intend to lay the track directly into the plywood. Not wrong but easier to make changes if you use cork or Homasote roadbed over the plywood. if you make the plywood roughly 3/4” beyond the outside rail then it could represent the ballast edge, and with a taper beyond this, the subroadbed. So about 1-1/2” + 5/8” or 2-1/8” +/- plus the slope beyond. With 1/2” plywood then a 3” width makes sense. Staple or hot glue cardboard strips to the edge of the plywood to begin scenery. 
 

Early era and backwoods railroads may not have had roadbed or even ballast so the width of the plywood would be anything easy to support and attach scenery. 
 

Another thought

I had mentioned spline roadbed. The scenery is attached to the side, below the track. And built up to that track level as needed. Depending on main or siding or branch where you decide how much ballast. So, I would have to guess that no matter what wood you use, or how wide. You could attach scenery to the side. Even pink foam could be stuck to the side. Although I'd rather use the foam instead of wood.Just MHO about foam. But, I hope this point is taken in the manner in which it is offered.

1 3/4 " sub roadbed in HO

I use masonite spline that is seven pieces thick or approx. 1 3/4". This gives me plenty of room to allow the roadbed to be just wider than ties.  I use gorilla polyurethane glue to attach XPS foam to the masonite. This forms the base of my scenery. 

It works for me. 

Thank You

Thanks for all the suggestions.  It's more helpful to make a decision when presented with a lot of options.

Don't forget to have enough set back from the edge of the bench

work to avoid the big drop to the floor!  Also consider the overhang of your rolling stock going around curves.  I can share an outrageous example from our modular club experience.  We were set up in a shopping mall quite a few years ago.  A guy who was friends with most of the guys in the club brought out a brass Challenger an asked if he could run it on our layout.  We did not mind so he put it on the inside main.  Going around the layout the boiler was hanging over the outside of the outside main on 48" radius curves!  Passenger cars, and large modern freight cars can have quite a bit of overhang.  That is not a problem if you have a single track with no scenery close to the right of way, but a double track meet can be disastrous.