Can they? Then why don't they do it already, instead of the expensive and difficult arrangement of out-basing UKBF officers in France and Belgium?
We have to be realistic that what is acceptable to all other European countries is not acceptable to the border authorities in "Fortress Britain", and that is not going to change. Given the long saga of migrants in Calais attempting to avoid claiming Asylum in France in favour of Britain, it's not entirely unjustified.
The new portable passport scanners are good though - I saw them recently when entering Ukraine from Poland on a sleeper train and it's a great time saver compared to taking away everyone's passport to be scanned in an office elsewhere.
To expand on your remark about migrants and asylum seekers part of the reason for the frontier controls is that there are some fundamental differences in the way that the state relates with its population. In the UK it is not necessary to register one's address with the local authorities whereas in most, if not all, of the countries within the Schengen area, this is a legal requirement together with each individual being issued with an ID card of some sort[1][2].
The Schengen agreement generally allows nationals of the countries making up the area free passage of the borders but when in another country the individuals have to carry the identification required by that country for its own citizens.
The UK does not require its citizens to carry identity papers of any kind and as states generally have the right to refuse entry for certain categories of people the only place where identity papers of people coming from abroad can be checked is at the frontier.
Until the UK introduces a requirement for its citizens to carry ID, thus meaning that ID checks can be made anywhere within the country at any time, then the frontier controls will, as you suggest, remain.
[1] The nearest the UK gets to requiring an address to be registered is that sub-set of people holding a driving licence - any changes have to be promptly notified to the DVLA.
[2] Some years ago - about the time the Schengen arrangement was being discussed - I heard someone[3] saying that this difference was due to the state being seen in the UK as a construct which was intended to serve the people and in other places the people were to serve the state.
[3] Unfortunately I can't remember who it was or where it was said, but it was some form of public meeting.