Quite true, any intelligent player is going to rebuild after cancelling the upgrade... But usually the right course of action is while your slingers are destroying the tc, build a stable and get scouts... Otherwise you have food (I'm assuming you still have an econ after slinger rushing which you'd better) and wood sitting in the bank. Hopefully you find their new base. If not, keep searching and try to find base while simultaneously taking out any tool buildings that they have build (make them waste more time and wood rebuilding those buildings). If you still haven't found it, well, you're in trouble definately... keep searching and destroy houses (waste more vill time + wood cuz they can't get a military in bronze without housing). And hopefully you find them in time to get your slingers at their econ... Theoretically though if you haven't found their new base and they bronze, you're doing pretty badly... But you did remember to wall in didn't you ? So after those first 2 or 3 scouts you should be getting food in and walling like mad... because you have stone (you need to be mining for tons of slingers)
Maybe you can survive to get to bronze shortly after them. At very least, you've caused them to run to a remote corner of the map (ie wasted villager time) rebuild a tc and hopefully a tool building and a few houses plus a new storage pit (ie 400-500 wood is very difficult for a fast bronzer to save up... boomers on the other hand....)
If your opponent sees your barracks , you need to produce axers as soon as they start boning slingers... Or if you're like me and don't do good enough scouting and end up building your barracks up against the enemy's town center (I did this earlier today lol) Axers are your last resort.
In any event when you all out tool rush, your first priority is to make sure the enemy doesn't get bronze. Second priority is to make sure the enemy doesn't have the econ to do anything if they do get there. Normally if I don't do SIGNIFICANT damage to my opponent's economy, I don't even think about bronze (the obvious exception is a team game).
Now in a team game, bronzing in a reasonable time is important... You can't commit to an all out rush (unless you know your partners are rushing also). But you can still bronze in a reasonable time (17 min) with a decent slinger rush (while at least hurting one opponent). As has been pointed out, make sure you know your partners and their competence level. It's much better to do a standard bronze boom when your partners aren't going to see bronze any time under 25 minutes. As an example the earlier game where I was axing away at my opponents tc, took it out... (3v3) He didn't bronze till 30 minutes in as a consequence (I had killed 5-6 vills + some buildings too) However I hadn't bronzed (as I was rushing) till after I decided that I needed to be to defend from the other players (at about 20 min in I pressed the bronze button) Both my partner's reactions were "You're bronzing already!" And I knew the game was lost...
In any event slinger rushing is a tactic worth trying at times, but I'll agree that it's not a cure-all. Booming is much better a lot of the time. I'll agree it leaves you with a lot less options and isn't very flexible. But neither is Axer Blitzing... It works given the right situation. As someone else mentioned, it's just another alternative to add to your list of options.