Is there any problem with running tubeless on non-tubeless rims? I have Fulcrum 5 DB wheels, which are not tubeless ready. My previous wheelset were tubeless compatible and I've been impressed with running tubeless.

So my question is: Assuming I can mount my tubeless tyres on the new wheels and can get them to seal and not leak air, is there any reason I shouldn't run these wheels tubeless? Is the rim going to 'hold' the tyres less tightly and cause roll offs? Is there something else going on with tubeless compatible rims that I've missed?

My tyres are Schwalbe Pro Ones
One of the considerations (assuming you are able to get a good seal) is that air loss under a tire burping may be worse than a tubeless specific rim.  In CX this is definitely a consideration, especially if you are pushing the lower limits of tire pressure (e.g., &lt; 30 psi on 700x33c is amazing on slick off camber turns, but it is easy to fold the tire in a hard high traction turn).  A large burp could drop the pressure dangerous low, resulting a loss of control and injury.

For running on the road, it is unlikely you will want the pressure at such low levels, so burping events are much less likely. [DISREGARD - see Update]

Update - Nov 28, 2016

Found this quote from Lennard Zinn:


  When using road tubeless tires, I recommend using tubeless-specific
  rims. For the lower pressure of mountain bike tires, I think, other
  than a bigger burping issue on corners due to the lack of the
  bead-locking “hump” on the medial edge of each bead shelf, that
  tubeless conversion with most rims is fine. 
  
  Read more


For road bike applications, Lennard recommends only using tubeless-specific rims, but for mountain bikes (read larger volume tires) this is not always necessary depending how low of a pressure you are running and how aggressively you are riding. Similar to my initial answer, Lennard also points out you stand to lose more air in a burping event.

Thinking about Lennards answer some more, I suspect his recommendation for road tubeless has to do with a lower margin-for-error with a road tubeless tires. You are dealing with smaller air volumes, and are much more susceptible to negative consequences associated with air loss events.  

For example, you could have a poor rim/tire seal.  It seems to hold air at initial inspection but it is in fact slowly leaking air. Air loss during a ride  could result in the bike becoming uncontrollable.  With a larger volume tire, slow air loss is less of an issue because your margin of error is larger.  Small volume tires could reach critical pressure levels much quicker than a larger volume tires under the same poor seal scenario. 

Because road tubeless tire a smaller pressure buffer, mistakes in your setup become critical to safety as critically low pressures can result in a bike becoming uncontrollable.

Conclusion

I would follow Lennard Zinn's advice and only uses road tubeless tire with a tubeless-specific rim.