This is where the US is somewhat 'backwards' compared to other countries in regards to ionising radiation (IR) legislation.
In the UK the Ionising Radiation (Medical Exposure) Regulations 2000 and its amendments legally requires (when at all possible) that non-ionising imaging modalities be used. There may also be (not entirely certain) a legal requirement to monitor dose given to patients during an examination (however, this is complicated in CT examinations due to how the machine operates and the numerous ways in which dose can be operated) which is performed normally by imputing the dose on the same computer system as the other patient's information. Additionally, there is legal obligation for those who carry out the examination (the operator) to have sufficient knowledge of what they are doing to deem the exam justifiable or not; the operator may include Radiographers (in the case of Radiographers, most of whom are going to be performing the CT, X-ray, MR or US exam they may refer to a Radiologist if they are uncertain to whether it should be performed or not).
Another part of justification is viewing the patient's exam history; now because hospitals are linked electronically, it's relatively trivial to transmit images via a PACS system to another hospital, so if the patient had a CT head three weeks ago, the exam need not be repeated and really ought not to be unless the patient's condition has dramatically changed or if it is an acute case. Once again, the information can be stored on a computer and retrieved easily time and time again preventing the patient from being over-exposed.
Then there are the ALARA and ALARP principles regarding dose and exams - "as low as reasonably achievable" and "as low as reasonably practicable" which basically are self-explanatory.
It's not as simple as saying that there should be a dose limit for patients and that should not be exceeded. What if there is an obese patient, who will not fit in an MR machine, thus a CT machine must be used has cancer? From the staging and monitoring of the cancer his dose is likely to exceed the limit very rapidly. Patients in theatre or a Cath lab having an operation or pace-maker inserted can have doses in excess of 1000cGy due to complications of the exam or difficulty due to patient. So having a limit for people who may need repeated exposure to monitor and track pathological changes isn't entirely sensible (nor is it not without merit either).
Again considering patients: with an MR scan the child has to be as still as possible - if it's a small child or an uncooperative one (let's face it a child being caged in the MR coil, fed through the bore and lying around in an environment which has incredibly loud knocking noises ongoing for 20+ mins isn't great if you're a child) moves even slightly it can corrupt the entire scan sequence being undertaken due to how the images are obtained (k-space filling); whereas a CT can reasonably scan the entire body in a few seconds. Additionally, MR, nor US can be used to image the lungs so if the child (or patient) has lung pathologies it can't be demonstrated, therefore an ionising modality has to be used. Once again, the referring clinician should be considering these things when requesting the exam and other doctors (Radiologists) or Radiographers should be vetting these to ensure that they are deemed suitable
Quite frankly, the machines for the most part shouldn't be protecting the child in question - the operator of the machine should have sufficient knowledge to know how to use the machine (especially in the plain-film role) that they shouldn't be exposing if they do not; this again is in addition to other healthcare professionals doing what they ought to be doing.
It's not as easy as saying ionising radiation = evil. Any doctor requesting the exam should be aware of the dangers of what they are wanting to put the patient through and the risk-benefit should be determined. Other measures such as operators having to justify the exam; exams being vetted and protocoled by a Radiologist prior to the exam commencing; and application of rather basic radiation protection measures can protect a lot of people without having to instigate hard-limits into the machines; hell most of the manufactures are constantly working to curb exposure (especially in the case of CT machines or technological developments - shift from conventional radiography to computed to digital allows for lower exposures as the detecting medium is far more sensitive) without legal imperatives.