Recently, I got the following message from my bank:
What?!?!? A $15 000 credit card limit. That doesn’t sound very frugal, does it?
Poopsie and I had an account with $5000 in it that we had loosely termed our emergency fund. We also had a credit card with a $5000 limit that we paid off every fortnight, as well as a reasonably high cash flow from our salaries, so we were confident we would be able to deal with anything urgent with these resources.

Not an emergency!
However, it had been bugging us both to have that $5000 just sitting there, not invested and working for us. So we decided to increase the credit card limit and immediately transferred the $5000 to Vanguard. Now, we are covered for emergencies (even more than we were before) and our $5000 is compounding for our future.
Please note that this only works if you are disciplined with your credit card usage. There is no point having a credit card as an emergency fund if it is just going to carry debt. If you don’t/can’t pay your credit card off in full every month than use something else as an emergency fund.
Do you have an emergency fund? How is yours set up?
I’m working on building our emergency fund at the moment. It’s in a high interest savings account that is earning just under 3.5%, which is fine while we are building it up and I’m still educating myself on investing. I like your approach, though. Like you, we’ve always been excellent with our credit cards (never paid interest), but I did used to get a bit heart attacky when they offered to raise limits to ridiculous heights, so I got rid of them all. I may well consider this approach when I’m ready to jump into investing.
I think if you’re good at paying off your credit cards, then this is a great method. I usually just ignore credit increase letters. My credit card is through my bank (NAB) and you can actually switch off credit increase offers- maybe yours has a similar option?