Darren A lot of the specifics are hazy these days, it's been that long, but I definitely do remember enjoying the feature. I remember I'd try to use it daily. I remember some of the events- I actually still have the Cotton Guard Banette from a Halloween event! I reset for one that ended up with a Sassy nature and Hidden Power Fighting, ended up with a moveset of Cotton Guard, Calm Mind, Shadow Ball, Hidden Power. Sadly, if I move her out of Home, she loses Cotton Guard, but even still, very cool memento from that time.
To go a little more on-topic, unfortunately, I can't claim to have had similar experiences with Mystery Gift and the Trainer House in Gen 2, quite simply because I didn't have anyone around me who also played Pokémon during that time. I knew some neighbor kids during the Gen 1 days who were a big help to me when I was still learning the ropes, but I think they moved away by the time I had Gold and Silver. I did have a Pocket Pikachu Color, though, so I was at least able to spend Watts to get items that way, though if memory serves, I didn't have the patience to save up a lot of Watts LOL.