Product should, definitely, run user research along with Product Design. But what I find is that people in either have a problem imagining a solution that's a couple of orders of magnitude easier to build, but also much easier for our customers (usually boils down to making the right choices for customers — the savings are not in the common "choose good defaults", but in actually removing flexibility that's needed only in 1% of cases).

Thus, I insist on engineering being involved early to put real world constraints on wild ideation ("it would take 3 months for 5 engineers" quickly changes what's a must-have :)) — sometimes, a curious, critical mind can expose things like these without having to do the research or user testing themselves.

Now, throughout my 20 year career, it's been very rare to find a product person who will both understand customers deeply, tie their needs to business value, and be able to formalize the intersection of these in a form of good requirements for design and engineering to eventually build!

So I really believe an engineer's (and design) role there is to serve as a sanity check as they dive into actual building — does this really make sense? If they do not, they run the risk of a project completely failing or perhaps not even shipping once someone else questions the value of continuing to invest in this 3 month project 9 months in. ;-)

A business does need a small number of their most senior engineers doing high altitude work that can, at times, include helping sales estimate new features. But in my experience, it's not rocket science and a good product team can do this on their own with a quick async check over chat. At most, a single meeting is all it takes.

I've heard of Sales Engineers as well, embedding programmers directly with sales teams.

But the vast majority of programmers should not be spending any significant amount of their time on this. Their value is in building and scaling well-specified systems.