I tend to be hesitant of this model, but I've seen it work. It depends on the team and the people.

In the cases where it works the hallmark of success is a team that is highly engaged. If it's a start-up or a company where everyone has a vested interest -- financially -- for the company's success, the probability that it'll work is high. The probability that eliminating the formality and just letting everyone work from home all the time will work is also high, though. Maybe the schedule is useful because in-person collaboration is so deeply needed for the remaining days that it's worth keeping to a smaller schedule for work-at-home[0].

Where I've seen it fail was at a few larger employers where engagement was moderate/low. Many of the employees were working their exclusively to collect a paycheck and didn't have a lot of passion for the work they were doing. The "work at home" day was really "a day off". Management scheduled this day to occur two days after the weekly release cycle -- the one considered to have the least impact after a release where employees not being available on-site was going to be less of an issue. The problem with that thinking was that it further encouraged the mentality that it was really a day off not a work from home day. I'd hear stories from my friend about how he'd schedule all of his personal stuff on that day -- he'd take the kids places during the work day and otherwise do things that he would not "get away with" in the office. This policy stopped after about a year because enough employees abused it. Unfortunately, for those who didn't abuse it, they got punished.

By making it "part time", you also have less pressures to put in place the tools necessary to make work-at-home successful. Highly motivated teams won't suffer because they'll naturally gravitate toward tools that make it possible to complete work -- getting the work done is the driving factor. Unmotivated teams will fail because that driving factor is missing and will be filled in with an attitude of "well, I can't do this because there's no way to get what I need to do my job, so I'll sit on it until I'm back in the office". There's also the issue of not having parity between the equipment in the office and the equipment at home. If you have 2 workstations at your desk in the office and a laptop -- you're probably using your workstations at work and rarely using the less powerful laptop. As a full time work-at-home employee, I have two servers with several virtuals, two laptops and a very high-end desktop ... at home. I'm full productivity all the time. Yes, you can probably remote into your workstation at the office. It's not the same -- I've tried it -- maybe it's the lack of three monitors in your home office or the network latency of the remote desktop, but something just makes it "less than".

By making a schedule, you're also forcing employees who might not want to work from home to work at home. It sounds crazy, but over the years I've met several software developers who don't fit the stereotypes -- they'e extroverted and enjoy the office. They see the office as an extension of their college life where they had a bunch of friends who were forced to get together -- in person -- and get along and feel lonely working at home. I might have been one of these people -- I get lonely from time to time working at home full-time but have found ways to combat that.

On the flip side, there's potentially a benefit to the forced schedule for introverted team members or folks who require intense focus to accomplish work. They'll most likely drop completely off the map when working at home because they can isolate themselves completely and pour into work. Keeping some in-office days helps those personalities get pulled into the larger team and can focus on the at-home days without interruption. We had a member of a team I was on a few years ago that worked at home two days a week and we knew when he'd return on Wednesday that he'd often come back having completed a mountain of work. We knew those days benefited him and the greatly benefited the team so if he asked to take another couple in a particular week, nobody ever questioned him.

[0] I'd argue that 4 days at home working and one day dedicated to pure collaboration would fit better, but it depends on the work/team.