Is it valid for the first hire of a pivoting startup to request a cofounder position and a matching equity?

Co-founders should not be created or added to stroke an ego. They should be added because it is advantageous to the business. If the engineer was dedicated to giving their full focus to the business before the pivot then they should be just as dedicated after the pivot. That doesn't mean that some small equity incentive can't be added, but matching equity and co-founder title. Why? Your employees will come up with a lot of great ideas. That is what they are paid for. In this case what has the engineer added to the business other than their ego if you make them a co-founder? Were they going to withhold creative ideas before? That being said, if there are other circumstances at play that Balaji brings up (like they aren't being paid) then you need to consider that as something they *are* adding to the business.

I think it's probably a fair request from a logical point of view, but it's not a good idea.  If you have only known this person for a few weeks, it's hard to say for certain this person will work out - what if they turn out to be lazy, or less talented than you thought, or just generally not interested in the new idea? Co-founders are co-founders because they trust each other, and often have worked together before.  That being said, maybe meet the engineer halfway?  Give him the cofounder title, since that's largely meaningless anyway, but keep his equity the same.  Or do an option grant with a 12 month cliff vest - so if things go well, he gets made whole further on down the line.