I criticized the Persona 3 Social Links system quite a bit last time, so this time I think I will offer a few ideas on how the whole system could have been designed differently to get a better result. A lot of the fundamentals are very solid, such as the ten levels for each Link and the corresponding benefits, so I will keep those intact. Some other things, though, really need to be changed.
I think the most important change would be to put more emphasis on the effort needed to unlock the events that raise Social Link rank, rather than on the events themselves. It should be a bit harder to raise rank, but the process should be more interesting. This means that the kinds of scenes you see when hanging out with a friend on a Sunday in Persona 3 should replace the empty and generic "you feel your friendship is growing stronger" scenes you see when hanging out with a character who isn't ready to raise rank yet. Overall, you should need to interact with a character fairly often in order to build up a Social Link, perhaps as many as thirty times or more to reach rank 10, with even more scenes available than necessary to reach rank 10. This many scenes gives a lot more space for good character development.
One problem with requiring a large amount of time like this, though, is that it might make it too hard to build up a large number of Social Links, but this problem is easily solved by making it easier to build up many Social Links in parallel. In other words, I think the Persona 3 system of only hanging out with one character at a time should be abandoned (since that system is itself something of a limitation, this is killing two birds with one stone). Thus, most of the time you will hang out with two or three people for an afternoon, rather than just a single person. This has a side-benefit of enabling more interaction between the different Social link characters, which can help add some depth to the characters and keep things entertaining for the player.
Another major change that needs to be done is to add some obligations for the player to uphold, particularly regarding clubs. I really think that the player should be expected to go to club regularly, rather than treat a club as a simple opportunity to hang out with a single friend. Thus, I think the player should deal with the risk of having his Social Links enter Reverse state if he doesn't attend club regularly. Of course, that kind of punishment is impossible in Persona 3, since it is expected that the player joins at least two clubs, a sports team, and Student Council, which each meet three days out of the week and have conflicting schedules. As such, in my ideal system the player would only join one club, and this choice would mostly affect the speed at which you build up Social Links, rather than what Social Links are unlocked.
At this point, I think my full ideal Social Link system has begun to take shape. In this system, your choice is not "who will I hang out with today" but rather "what event will I see today". On any particular day there will be several different events occurring, each of which involves a few Social Link characters. Maybe on one day Yukari and Fuuka would invite you to go shopping with them, Kenji, Junpei, and Bebe all decide to go to a restaurant, and Student Council has a meeting, while on another day Akihiko and Junpei go weapon shopping, Chihiro and Mitsuru go somewhere to talk about ways to help students who suffer from Apathy Syndrome, and Yukari and Yuko are at Archery practice, and the player has the choice to watch any one of these scenes (which may never appear again in the game). At the beginning of the game, you choose which club to join, each of which has several characters associated with it, which lets you interact with those characters far more regularly than would otherwise be possible, but obliges you to attend club regularly at risk of alienating your friends. When you have built up a friendship enough, you can see a special event and build up Social Link rank the next time that character is free.
This system has a few advantages over the Persona 3 system. First, because every day has its own events, the characters can actually respond to the flow of the plot and different days of the calendar. It also fleshes out characters in ways they could not be in Persona 3, so basic character traits like "who are Yukari's friends" or "what does Akihiko do all day anyway?" can actually be explored. It basically lets fun events like the Yakushima trip or the impromptu comedy routine become the norm, rather than the exception. Another major benefit is that would a lot more onto the replay value of the game, since different choices would let you see almost an entirely different game on a second time through. Of course, there is a fairly substantial disadvantage for the developers, since such a system might demand more than a thousand Social Link events in order to offer reasonable choices for the player each day, rather than four hundred or so in Persona 3, so this scheme can hardly be called perfect.
There are just a few more minor things I should mention. First, I think every member of SEES in Persona 3 should have had their own Social Link, not just the girls, so that is one other thing I would have changed. Also, I would add a benefit to hanging out with a person whose Social Link rank has already been maxed out. Something basic like small stat boosts or experience point bonuses for Personas of the same Arcana would be appropriate.