Why is max power time limited for jet/piston engines?
Maybe Nothing.... 

Maybe Catastrophic Failure...

Any number published by an engine maker (or any aviation part maker for that matter) is the numbers they have tested it to. Thus if Continental or GE claims a 2000 hour TBO but puts a 5 minute limit on max power, that in turn means that the 2000TBO number is based on operations within these published limitations. Exceeding these limitations may cause TBO to arrive sooner than expected and could possibly cause undesired operating characteristics. It is of course possible that if you drive the engine at max power for a time greater than suggested, it will throw itself to pieces. However, this is unlikely. 

In some cases there are physical limits based on the materials used in the engine. If exceeding maximum run time provides a way to generate internal temperatures that exceed the limits of an internal part you could very well have an issue very quickly. From my experience with piston engines it's generally a wear and heat fatigue issue when flogging the engine at max power. That being said if the POH calls for a maximum of 5 minutes at full power and you spend 5 minutes and 30 seconds at full power on a climb out chances are you will be fine. If you do this routinely you may find that your engine hits TBO long before the published numbers.   

This article also alludes to the fact that there may be other limiting factors such as the strength of the gear box the engine is connected to. 


  The shp of a turboprop engine is restricted by the strength of the gearbox that drives the propeller, and by the ability of the airplane to handle the thrust developed by the prop.


On any note I would think that most manufacturers publish numbers that are on the conservative side for many reasons.  

Since this question is highly related to TBO number you should check out this article about some common myths around engine overhauling numbers and engine wear in general.  

Definitions: 

TBO: Time Between Overhaul. This is generally the lifetime of an engine. Although some people commonly think this is a legal number it is only manufacturer suggestion and you are free to exceed it (and plenty of people do). 

POH: Pilots Operating Handbook. The document that outlines the limits and safe operation of a given airframe.