The Arduino can only process one interrupt at a time, so everything else that uses interrupts will not work, some realworld examples -
millis and micros functions use interrupts, so will become unusable
The servo library also uses interrupts and will become unusable
Interrupts are a generally assumed to be time sensitive and everyone who writes code for others to use has this generally understanding that they will be in and out of interrupts as quickly as possible and so will the users of thier code.
If anyone starts to 'hog' interrupts, everything starts to fall apart - apart from that its easy to avoid doing so there really is no advantage or justification for long slow blocking interrupts.
Bit more information here -http://rcarduino.blogspot.com/2012/11/how-to-read-rc-channels-rcarduinofastlib.html