I think coming in to the office 1x / week would let you live quite a bit further away than coming in 5x / week. At least for me, I could do a 60-90-minute drive to work 1 day per week, but would not want to 5 days.
I had a job for a bit over a year where I commuted 90+ minutes door to door many days. Even though I could take the train if I wanted to (after driving to the station), it still got old and I wouldn't have wanted to do it long term. I'm about the same to go into my company's Boston office now--I'm technically out of our suburban office and in practice I've been remote for a few years--and it makes for a long day but one day a week would be pretty doable.
But for what benefit? Will the office be full sized (forfeiting the cost savings to the business), or will teams have to negotiate which days they’re supposed to come in (forfeiting a large amount of the team building benefits).
It just seems like a lot more work and hassle than being fully colocated or fully remote.
Teams schedule conference rooms. Even fully remote, teams will presumably get together physically a few times a year. Whether you're "fully remote" (and maybe have to fly to a get-together) or schedule weekly/biweekly office time will be a function of how a team/company wants to operate.
There’s a huge difference between a few times a year and once every 1-2 weeks, both on the company and the employee. At once a quarter we can just rent a coworking space and fly in, but at once a week everyone needs to live within ~90min of the office and the company needs to maintain some level of excess office capacity in order to seat these workers 1x a week.
To my eye remote 4x a week forfeits most of the benefits of full remote purely for the sake of a vestigial habit. It seems superior to me that either the team either goes full remote, or reverts to a “remote work when errands require it” arrangement.
I don't necessarily disagree and, in fact, you're describing the way that my broader group is organized albeit with some subset of people normally going into an office.
That said, there are plenty of people who want to go into an office semi-regularly and, if you tell them they're going to be 100% remote--even if financial arrangements are made to subsidize a co-working space in some manner--they're probably not going to like it and will probably leave for a more office-friendly company.