For starters, it might be useful to distinguish "push/pull" and "push/pull/legs". In PPL, the legs get a separate day. Let's assume PPL for the rest of this post.
The way I see it, but I could be wrong, is that for the intermediate or advanced lifter (it isn't that great for a novice) PPL is simply very convenient. A novice would want to do 3 full-body workouts per week because they can recover from that, but in the intermediate stage that's often no longer really feasible, or at least not in a way without intra-week cycling (say, intensity on one day and volume on another). PPL provides the following:
- Separation of muscle groups. Push would be benches, overhead press, triceps work... Pull rows or explosive pulls, pull-ups and chin-ups, biceps work. Legs would be squats and/or deadlifts and maybe assistance. That leads to...
- Enough recovery. Finish a push workout and the corresponding muscles get several days of recovery before the next one. If you did benches one day and overhead presses the next, the triceps get worked two days in a row, or with only one day in between. 48 hours might be enough recovery for a novice, but for an intermediate that OHP would suffer from the previous benches and you're cutting into triceps recovery. Also...
- Workout efficiency. You might need less warm-up on your OHP if you did benches first, and no warm-up on triceps isolation work, because your workout is focused on one muscle-group and there's some carry-over in the warmup. Same for squats and deadlifts. If you're not averse to doing both on the same day, squats will already warm you up pretty well for deadlifts, meaning you'd need less warm-up sets on the latter.
- Workout length. An upper/lower split can lead to long workouts, especially on upper body, if you want bench presses, OHP, rows, pull-ups/chins AND some assistance work in the same day. PPL is at its basis taking the upper day and splitting it up. Great if you have limited time in a day.
- Convenience of scheduling. You could do each workout twice per week (PPLPPLx, with x a rest day) which gives you a weekly schedule, or go for an average of 5 workouts per week with specific rest day intervals. Example: week 1 could be PPLxPPx, week 2 LxPPLxP, week 3 PxLxPPL, week 4 xPPxLxPP, week 5 LxPPxLx, and week 6 would be back on the week 1 planning. Or, if you like to work around your weekends, how about this: week 1 is PPLPPxx, week 2 is LPPLPxx, week 3 is PLPPLxx, and on week 4 you've looped back to the week 1 schedule. There's a lot of possibilities, but you still get 1.6 workouts per muscle group on average each week with both options. Less intense than 3 full-body workouts per week or 4 workouts per week in an upper/lower split (2x per week per muscle group), which might be too intense for the intermediate and advanced trainee. But you get more than 1 workout per week per group which is sub-optimal for the natural trainee. You can adjust scheduling based on recovery and the intensity you can handle.
- Because you can go for 2 workouts per muscle group per week, or 1.6 (or even a different spread) a PPL routine can be adjusted over time in scheduling to aid in the recovery that gets harder and harder as the weights rise. It works for the new intermediate and more advanced intermediate alike!
- As a template it allows for variation. You could have the first push, pull and leg workouts of a micro-cycle of 6 focus on volume, then the second push, pull and leg workouts of that micro-cycle focus on intensity. Doing that builds on a basic concept of the Texas Method: use volume conditioning to provide a stimulus and then, when you've recovered from it and your strength baseline has shifted up momentarily, use it to go hard on intensity.
Also, statistically, most lifters who are serious about their workouts and don't give up after a couple months or a year will be intermediates. The novice phase is usually over after 6 to 18 months, but the majority of recreational lifters won't get to the advanced stage, which is usually the domain of competitive athletes. So if you scour forums and other online resources, you're bound to run into a lot of folks who've gone on a PPL routine.
I'm currently doing an upper/lower split where the first two days I do an intense lower and intense upper workout, and the last two days to a lower and upper workout with some more volume and assistance. Sometimes a workout ends up taking more time than I'd like, particularly the upper ones. When thinking about a way to maybe spread it out more, the most natural idea that came to me was something that essentially is PPL (although I'd prefer an LPP order). As your workouts get more complex and some cycling starts to become necessary, it is desirable to spread them out over more days. PPL almost comes naturally then.
So the way I see it, it's a pretty natural and logical progression for people who've left the novice phase and exhausted their progress on a transition program, rather than something inherently beneficial to the routine itself. The ones you mention, Madcow and Ice Cream Fitness, seem better for a novice or to transition from a novice routine into intermediate. ICF is absolutely a novice program. Madcow shares some superficial similarities with the Texas Method and is more an intermediate program. On the Powerliftingtowin review, it is stated that it seems better suited to a late intermediate lifter and I tend to believe the judgement on that site. Most people out there who aren't after big powerlifter totals want muscle hypertrophy, and PPL just seems like a much better fit than, say, Madcow.
If folks have actual scientific insights into the efficiency of PPL routines, that'd be pretty great. But I'm afraid a lot of studies out there will be too limited in length, or focused on novice lifters, to really provide insights.