You can make your portico in timber, of course. The questions are,
Can you make it structurally sound?
Can you make it look good?
Can you maintain it?
This is the bay window of a Victorian house in my road
The original columns were stone; the ones in the picture are new timber. The bay was rebuilt by a company called SPS Timber Windows. They've done a very good job here and on other houses; you would not suspect that the whole thing isn't original stone.
The columns sounded hollow when I tapped them, so I assume that there are structural supports inside - such as a scaffolding tube or an Acro. I don't know if the lintels are timber or stone.
I don't know what timber has been used; I'd guess marine ply for its weathering qualities. All the edges are very clean and accurate - obviously machined - which is vital for the detailed look and the overall appearance. That's difficult for an amateur to achieve in plywood.
The timber here seems to be treated and painted, not plastered. The mouldings are machined wood, I think, though they could be cast plaster, like ceiling roses and cornices.
The job cost £000s, and if it were mine I'd be worrying about it all the time. The tops of the columns are flat(ish) so they'll be water-traps. The columns are sitting on a stone sill with not much fall, so that's a rot-site. All the vertical edges might move and crack, allowing disastrous water penetration. Sun and rain are very corrosive elements, as you know. The columns, the lintels and the window frames are all liable to move with respect to one another and to the house. The Victorians used stone - even on these relatively cheap, somewhat jerry-built houses - for stability and durability.
No doubt the company has thought of all this and might offer a warranty, but that must depend on the owner's maintaining the structure very carefully.
I hope this helps you think about your portico. You can do it but you've got to do it very well or it'll look very bad.