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