I live in South Africa where violent crimes are quite high, most of them involving some sort of weapon - be it unlicenced (usually) firearms, knives or other means. I am involved in the healthcare industry and spent many years working in A&E Departments and the prehospital environment. What I can tell you is that many stabbings were commited with homemade "shanks", screwdrivers, and even broken bottles (which do a surprising amount of damage). The point I'm trying to make is that so-called "legal" knives are not used as weapons by people who do not have the means to purchase them - and actually the homemade weapons which are then substituted (by say a teenager who could not "legally aquire" a knife to use as a weapon) do far more damage than than the real thing.
In fact a screwdriver to the chest will generally be much more lethal than a stab wound by a knife. And many times the wound is hardly even noticeable.
It's interesting how patterns of violent trauma vary from society to society.
I work in an operating theatre, often dealing with trauma. In 20 odd years doing this sort of work, I have never had to deal with a violent gunshot wound (meaning one that wasn't either accidental or self-inflicted). Not one. I have dealt with a few knife attacks, and attacks with blunt weapons, several of which were very nearly fatal.
A few years ago, there was a spate of "glassings", where people would smash a beer glass or bottle and use it as a weapon in a pub (bar) altercation. These can produce some pretty awful facial and eye injuries. High risk pubs now use plastic glasses and I haven't seen a glassing injury in several years.
I see lots of blunt facial trauma (inflicted by fists) and a bit of hand trauma (inflicted by faces). Most of the victims and perpetrators are being d**ks and alcohol or drugs are usually involved. Fairly uncommon that anyone dies though.
I don't know if the different patterns of violent trauma are primarily related to the way the society works or the availability of weapons or perhaps a bit of both. In my experience (in Australia), the significant majority of violent trauma is not premeditated but the result of a heated altercation or an over-reaction to an insult, often when people are affected by substances which reduce their impulse control (often in people with fairly poor impulse control to begin with). Minimising the damage that can be done in this situation seems sensible to me (especially if it keeps me in bed in the early hours of the morning). I do suspect that if those idiots who were doing the glassings (and nowadays are just using fists) were carrying firearms, I would have dealt with a lot more gunshot wounds. And been out of bed in the wee hours more often.
Your country may vary, I don't know.
There is often a trade-off to be made between liberty and safety. Where that line should be drawn is very situation dependent and should take into account the magnitude and frequency of the risks involved, the degree of imposition on individual liberty and the way that the particular society works. Taking one extreme, I don't think it's sensible to ban the use of kitchen knives because you can't prepare food propperly without them. And, as has been mentioned, improvised weapons can probably do almost as much damage in determined hands. Taking the other extreme, giving everybody access to weapons of mass destruction would be ridiculously dangerous.
FWIW, I suspect that the proposed UK ban on mail order knives will not achieve much, but I don't live in the UK so my opinion probably doesn't count for much.