(I'm probably biased in all this because I've played every Sims version. Each version has had their relationship pros and cons, but I think all of them are superior to the current DF system. So this is just my two cents - maybe 2.50.)
I think what's desperately missing is an attraction system. Every dwarf has a need to spend time with both friends and family. But assuming either is present, dwarves make no effort to actually spend the time together. Very rarely I see a "fondness talking with a child" or "blissful after spending time with a friend". But for the most part I think these are accidents. It feels like there is an intent to seek out either or both as the need grows, just as they do with reading or socializing in general, but the mechanic is not programed yet. The same should apply to relationships. No matter a dwarf's preferences, there should likely be some other dwarf they're attracted to and seek out their company to improve their relationship.
But here's my take on what we have now and how to utilize it. The original seven dwarves start with a pretty high initial friendship - you can see it on day one of the embark. But during that first year, they also spend a whole lot of time with "no job" hanging out near the wagon. The wagon is a tiny meeting zone, and so they are always in very close proximity. I believe dwarves with "no job" build relationships with adjacent dwarves faster than any other activity as a relic from pre-tavern/socializing days. Without fail, in all of my forts in recent memory, some pair of dwarves have been lovers by the end of the first year.
As a fortress grows, and a larger meeting zone gets built, maybe a tavern goes in, and dwarves are assigned much more busy work, their chance of randomly being next to another particular dwarf becomes less and less likely. Hence less recognition and even lower chances of building anything higher than acquaintance. By the time there are 40 dwarves, and no special effort is made to engineer relationships, I believe the probability of a relationship forming naturally are near zero.
In recent forts, and my current fort in particular, I have increasingly incorporated more engineering into my designs, with some success. I tend to grow populations slowly, and allow nearly half the available time for leisure (meaning a completely clear job list). Most dwarves in these forts acknowledge most other dwarves at least - I'd estimate about half of them know at least half the other dwarves. There are extremes on both ends, a few know most everybody and are "friends" with about half, while some only know a handful with no friends. In my current fort, I got the single lover pair in the first year that I've come to expect. It was an FF pair, which wasn't too surprising with 5F/2M initial split. But what was surprising is that sometime in years 2 or 3, two more lover pairs formed from the initial seven - an FF and FM.
Anyway, I'm sleepy and getting long-winded, so let me get to the point. I believe that if you can replicate those first year conditions, in what you might call micro-communities, you would have what would appear to be a much more natural progression of relationships. Let's say you could keep eight dwarves of a similar age all working and taking breaks in close proximity, then eventually you should see them all be friends, all getting happy thoughts from spending time with a friend, and hopefully eventually getting some more advanced relationships going. By reducing the number involved, you would significantly increase the encounters with any other particular dwarf. While I haven't actually done this in my current fort, the design is set. Each z-level is a block of rooms and workspace for eight dwarves. Eventually, as I get groups of eight eligible singles, I'll set up a burrow ala honeymoon suite, just big enough and with enough commodities for them to all live the remainder of their lives. Then I'll let them go and see how well it works. I'll keep ya posted.