This is heavy handed, as is the client using this type of negotiation tactic. It's not healthy to respond this way.
A better solution would be to respond: "Well, my rate is based on my experience with XYZ and because I've been in this industry a while. A lot of developers out there aren't interested in this kind of thing and don't understand what you're going through. Honestly, I hired a couple myself last year and it took more effort than I saved just trying to get them ramped up."
Then just smile and leave it at that. Sometimes the best response is to make your point and not get into a conversation about it.
This is heavy handed, as is the client using this type of negotiation tactic. It's not healthy to respond this way.
Possibly I'm getting less mellow with age :-) My responses used to be more like yours, now I tend to be a bit more direct.
The ones who are approaching it purely as a negotiation tactic don't care or mind - they understand what the issues are and appreciate cutting to the chase.
The ones who really don't value my time I don't actually really want as clients...
However you approach it - and your approach is completely reasonable - the key realisation is that this isn't a question of the client not having the money to pay $dayrate. This is most likely a pure negotiation tactic to get a drop in the quoted rate.
A better solution would be to respond: "Well, my rate is based on my experience with XYZ and because I've been in this industry a while. A lot of developers out there aren't interested in this kind of thing and don't understand what you're going through. Honestly, I hired a couple myself last year and it took more effort than I saved just trying to get them ramped up."
Then just smile and leave it at that. Sometimes the best response is to make your point and not get into a conversation about it.