Many types of children's behaviour need an amazing amount of control by their parents - it's what children do! And as for embarrassment ... it will be your daughter who runs the risk of embarrassment, not you, if you stop taking responsibility for keeping her dry and leave her to do it herself. It sounds as if she is never completely wet because you spot the signs and whisk her off to the loo, and if you're doing that, rather than letting her take herself, then maybe you are taking away any motivation she has for going to the toilet herself. Maybe letting her embarrass herself would be a good way of making her think for herself - she has no reason to stop being lazy if you are always ready to do it all for her. She is only lazy around you, not the teachers - might that be because she knows the teachers won't take responsibility for taking her to the loo in the way that you do?
With regard to punishing for other forms of bad behaviour, this type of problem is a completely different thing to many of the other forms of behaviour which punishments work for. Too much emphasis on toilet behaviour, and punishing them for toileting mistakes, can lead to further problems in that area later on, which can be very hard to correct. Plus it's something that happens several times a day, not just occasionally, so you end up feeling constantly stressed out about it.
Also, it's not something that you can take full control of in the way that you can with other bad behaviour, so punishing in the same way won't always be possible. If she's pulling her friend's hair or smacking the dog you can physically make her stop, and punish her in a way that puts you back in control. You can't make her stop doing this in the same way so she remains in control of the situation, not you - even if you punish her, there is bugger all you can do to stop it happening again.
And maybe if you make her take responsibility for her own toileting, her embarrassment at being completely wet, cold and uncomfortable may just be enough punishment on it's own.
IMO the best way to deal with any kind of attention-seeking behaviour is to ignore it - and that's any kind of attention-seeking, not just this kind. When a child is attention-seeking they don't really care whether the attention is praise or shouting; any attention is better than nothing. So even if you respond with shouting and punishments, they have your attention and the behaviour worked.