Why does this hollowtech crankset have play? Background


Shimano deore crankset (not XT) 
The crankset has done about 10000km (6200miles).
It is from a touring bike. 
Most of those 10000km was done with the
bicycle loaded (bags on both front and back racks).


Problem

The crankset in the picture has play in the directions shown by the arrows.


However in this position (180deg opposite) the crankset does not have play.


I do not notice the play while riding. I notice the play when tugging at the cranks with both hands.

When I take off the crankset, clean everything, then grease and re-install the crankset, the play is gone but comes back after about 100km (62miles). The play does not seem to get worse.

On half of the inside of the crank (non chain wheel), there are teeth marks. The teeth marks are smooth as far as I can tell.

Here the marks.


Here on the other half no marks.


On the axle / spindle there are similar marks on the one side but not the other side.

Here with the marks. Again the teeth marks are smooth.


Here the half without the marks.


Questions


Is the play indeed due to a worn out crank? (I have not got the tool to remove the bottom bracket, so I cannot test to see if it is the BB)? 
Are the markings, or rather this type of wear normal? The original crankset was a deore XT which never had play and did about 20000km (12400miles).
When buying a new crankset, should I buy the more expensive or the less expensive? I was told expensive means light materials but quicker wear of the chain wheel, and cheap means heavy materials (metal) but the chain wheel lasts longer?
The marks on the splines look about normal. It's hard to tell absolutely from the pics. You're looking for any sign of deformation or rounding, which occurs if the pinch bolts are loose while riding. Always make sure the pinch bolts are nice and tight, 14Nm or about as much as you would ever put through a long-handled 5mm L-wrench.

You need to be able to torque-check your BB cups to go further. If one is loose that can cause all the issues you're experiencing. Replacing the BB entirely at this mileage is within reason too, although if it still works and feels great then by all means keep with it. Note they can have issues with looseness that's not accompanied by poor bearing feel. For example, the black plastic "top hat" of an HT2 BB can get cracked or come apart and preload will be erratic like you're experiencing even if the bearing feel is good.