That my internet friend is hogwash.
And just as equally is the assumption that you needed an additional post in between the post to post and house to post spans.

Rafters with a triple cut birds mouth (BM), a brace off the wall plate up to the ridge, and an engineered gluelam beam post to post would of allowed you to utilize only two posts for your covered porch addition.
To keep the same decking profile just move up to the next size 2by and make your allowance in the rafters BM cut.
To keep the same beam look look you could have used it from the house to post also, otherwise you could have utilized two 2x12's with 1/2" plywood sandwiched between and then wrapped all the beams with facia board.
I'm curious, what does your builder plan to use to hide the cave over your existing shingles?

Here's some pic's of the cabana at my house (equal spans as your post to post) and another one at a pool with cabana I just finished. Notice that in the pool cabana the triple cut BM rafter which slides down over the beam to not allow settling of the ridge. On really large cabanas like at my house I use engineered gluelam beams post to post, drop my rafters to the inside so to bear loading weight against the beam, then give up the standard jacks and commons, use mini beams laterally, then run an interlocking decking board from top to bottom. This delivers a very clean simple look to the ceiling instead of the ribcage look of standard roof framing. My cabana is almost a thousand square.

I'm curious, who spec'd a 20" center on your rafters?

See ya,
Kelly

Thanks Kelly,
I will suggest that solution to our carpenter.
However, I will have to check it through the permit police here. I like the lateral mini beam look. Very elegant looking. This is exactly what we had in mind when we start think about it.
One more question, does this design needs some sort of bracing at the beam corner (lateral bracing) becasue all the load is then concentrated at the corner and going downward and outward.

I sure hope this design pass the inspector test....
MrPluche

quote" does this design needs some sort of bracing at the beam corner (lateral bracing) because all the load is then concentrated at the corner and going downward and outward. "quote

Most definitely yes.

The load is always going downwards and outwards. That's why your man wants a brace under the ridge where it meets the hip rafters.
Make a mental picture of a triangle with weight on the top. The weight bearing down is all pushed to the sides, therefore your birdsmouth (BM) fastener (nail) is taking all the stress. This is dramatically reduced with a brace going straight down to a ceiling joist. As settling may occur the load is placed on the ridge brace. With an open air cathedral ceiling using the roof decking as your ceiling you have no ridge or purlin braces help distribute the load. That's why you triple cut the BM. It redistributes the load to both the fastener and the intersect of the inner plumb cut of the rafter and the beam. This allows the fastener, rafter, and beam, not just the fastener, to absorb the load.
On standard roof framing this load is divided by the total number of hip,jack, and common rafters.
When you go to the look like I have you gave up the number of rafters to divide the load by and dropped that number to either 4 hips or 4 hips and 2 commons. By placing the rafter inside the beam your quadrupling the amount of contact area to the beam and sending all the stress to the beam itself. The beams must be securely fastened to each other at the corners. I use a combination of large L brackets and nailing strips to fasten the beams to each other. I do this on the outside so they'll be hidden above and behind the soffit.
This look is still achievable on your project.

See ya,
Kelly

Thats some clean framing Kelly,intersting aproach. John

Thanks for the compliment.

This look is nothing new, it's very common practice in steel and large wooden beam commercial roofing construction.
I've always liked the clean lines and the very simple look it offered.
After I built a few of them behind some pools they just started selling themselves in spite of their higher pricetag.

mrpluche

quote" I sure hope this design pass the inspector test...."quote

There's no reason it shouldn't. I permit them all the time.
If you'd like to know how to blend this look into your existing deck profile let me know. Your carpenter should be able to look at the pic's and do it easily.

See ya,
Kelly