So until last summer, I've never had or played with minis. My game group, who have been played mostly online for over a year, got together for a live game (one of our number is in Texas). Everyone bought a mini before hand, some painted before hand, but most of us met up before the game start time and spent the morning painting/learning to paint. It was an awesome experience. Then playing on a board with minis was great.
I can def get why mapping and squares annoys people, but that doesn't remove how great playing with minis can be. Even abstractly, I think having a mini that represents you and your character adds a lot to a game. As for mats, I think they're neat, but by no means necessary or even warranted. I can always draw a square grid on paper.
And I don't think there's ANY problem using random objects for minis. I've played with dice, bottle caps, coasters... Friends and I used to play 40k using mostly poker chips and random objects (plus one broken Dreadnaught). It was great.