Step 1 don’t fully or firmly attach to the house (it must be able to break away)
Step 2 have independent supports by the house wall
Step 3 WAY OVERDUE water transitions , have an excessive amount of eave, expect that the slope will never be adequate no matter how much $$$ you spend , use a rubber roof or a single spray on that is fully waterproof even if water sits on it.
Step 4, use metal anywhere you can, if you go against better advice and use wood, use outdoor treated wood with thomsons waterseal especially in the roof and expect squirrels and other creatures will try to destroy your home using this area as a jumping pad.
Step 5, most important avoid having this be an insulated year round area if humanly possible
Yes myself and relatives have ignored one or more of the above resulting up to and including needing to later raise the deck or damage to the house main structure even though the thing was fully overbuilt past code)
Everything that can go wrong will and doing structural changes to mount into the house is extraordinarily bad if anything out of the ordinary happens(better to be out a deck than plow your main roof down after storm/tornado damage)
In the north these things are common and also always constantly a source of extreme pain and cost. Especially if the house brand new came with one from a builder.
If a contractor tells you xxxxx don’t believe them, better to overbuild it as much as possible YOURSELF unless you want a 10 year structure that becomes a boondoggle)
The contractors are correct. As a layperson short of redoing both roof lines it's a no go.
It’s not a no go but you are guaranteed to have non-recoverable storm damage down the road no matter how well it’s done and animals using it to burrow into the main structure, the slope no matter how steep is never enough to use normal shingle/construction methods.
That said, whoever designs homes with 3 overhangs in an area should be shot, homes shouldn’t meet code if they are designed that hillbilly way for aesthetics, up here that area WOULD LEAK at some point, likely invisibly making underlayment rot, total garbage design.