I'm usually extremely reluctant to use doubles past 2^52, when the minimum increment becomes larger than 1.0
Doubles larger than 2^52 are no different from smaller numbers in context of scientific computing etc. which is what floating point is for.
E.g. in a particular numerical simulation you could bump above 2^52 by using units of nanometers or below by using units of kilometers... yet this is likely just a simple multiplicative factor and the result of the calculation does not change one bit because of what units of measurement you use.
Getting closer to 10^300 and it is another story.