The engineer does marginally increase housing demand. They also increase local and federal tax revenue to support education, healthcare and other services. And the engineer will spend a large portion of their salary in the local economy, helping to support all the other business in Seattle. So there are also positive externalities.
What are some of the other "many negative externalities" you mention?
I feel like we could have the best of everything if you we just built more housing to keep up with demand.
It's just a never ending balance problem. Also the "just build more housing" is such a numbers only view. Anecdotally, everyone I've talked to hate budget cookie cutter apartment complexes; they're ugly, neighbor problems, noise, pets, etc. What people really mean is they want a single family house sitting on land, but you just can't have both.
I don't know what a "numbers only view" means. But I lived in Tokyo for a long time and I basically think it is an ideal city, and obviously there are lots of factors, but I think the single biggest factor is the abundance of housing. They have way more of it and it leads to so many wonderful things, like mass transit or an endless supply of little hole-in-the-wall restaurants, bars, and cafes in walking distance.
Look at how people vote with their wallets: there is an enormous demand for housing in places like Brooklyn. That doesn't mean we need to turn the whole nation into Brooklyn, but I think (given the massive demand) why shouldn't we have a few more places like Brooklyn, i.e. dense urban areas?
Most places in the US have a remarkably low population density; we can definitely greatly expand the housing supply with a little infill and still have lots of suburbs.