I completely understand what you're saying, and I sympathize. I'm so sorry that you've lost your kitty, but I take offense to your saying that the folks up at Animal Control have "no heart".
I think that they work very hard to do all that they can but unfortunately, like most of the other shelters around here, their hands are so often tied by circumstances they cannot, individually, control.
In a perfect world, they'd all be No Kill shelters. It is not a perfect world.
They are limited by funding, rules, and the fact that they are simply overwhelmed by sheer numbers! And, while there may have been a chance that, had time allowed, you and your kitty could have had a happy reunion, there are dozens upon dozens that DON'T have anybody looking for them.
I wish to God we could save them all! However, I think it's a little heartless on your part to accuse these workers (who are, after all, just making a living, doing the job they've been hired to do) of being heartless. I have no doubt that they go home each night, wishing that there had been a little more time, that they could have done a little bit more.