Entonox is a tool, and one that can't adequately replace morphine or other opiods, or ketamine / toradol in a proper pain management regimen.
It's relatively safe, provided it's used properly. If for some reason the patient is unusually sensitive to its effects (copharmacy?) then they will stop administering it, as their arm falls away from their face and the mask drops off. It has some specific contradindications in terms of disease processes exhibiting air-filled spaces, e.g. pneumothoraces, bowel obstruction, emphysema. If you don't invert the tank properly, or expose it to low temperatures, there can be issues with FiN20.
But it has some limitations. It's simply not as effective at controlling severe pain as other agents, e.g. fentanyl / morphine. The patient has to be conscious, and capable of following instruction and using at least one arm to self-administer. It causes a lot of nausea and dysphoria, which are limiting for some patients, even those in severe pain, as often a mild reduction in pain + dysphoria is a no sale. It's not commonly used outside of obstetrics in-hospital -- so supposing it works, and you get acceptable analgesia -- you now arrive at the hospital, and have to either wait for the hospital to give other meds (usually opiates, that you could have given yourself earlier), so that you can get your tank / regulator back. Or you need spares, and a mechanism to recover your equipment left with the patient. Ultimately this will eventually run out, and create a problem after you leave. The ER staff may well be unfamiliar with entonox, and not know what to do with it.
I like it, usually as an adjunct to morphine, for short painful periods. It can help for moving someone to the ambulance, providing its not too cold outside. It can be ok if there's a bouncy ride. But it's not a wonder drug.
The area I live in has much laxer narcotic control laws than in the US. We usually check tank pressure periodically, during unit checks, then record start and end PSI when it's used. Typically it's primarily used by BLS, due to the limitations mentioned above, and a general preference for opiates in most situations by ALS. It's a good option for services that have a long distance for ALS intercept or no ALS.
There have been historical issues with abuse, but it's a lot harder to divert than other controlled substances. There have been incidents where tanks and regs have been stolen, but this is a little like stealing a D tank out of the airway kit --- if it's gone, someone should notice quickly. It could be taken from a stock cupboard, but this should be caught by an inventory process, or increased use of tanks caught by ordering. The only incidents I know of with prolonged abuse have centered around small services where the person ordering the tanks is diverting them themselves.
As a drug of abuse the effects are also very short-lived, so unless your provider is huffing the second a call comes in, and there's a very short response, any intoxication is going to be long gone by the time they get on scene. I would think that while the potential for abuse exists, the potential for serious consequences are minimal.
Don't get me wrong, it's not a bad option for BLS, but it's not a morphine replacement.