Alexander-Arnold is, without question, an enormously gifted player, but may not be the right sort of right-back for Southgate. To talk about his improved form in the second half of the season or his defensive qualities is slightly beside the point: he naturally operates in a relatively advanced position, which is how he has been able to contribute 32 assists over the past three league seasons.
To ask him to operate deeper would be to negate the great strength of his game, but playing high means there is space behind him that opponents can exploit – as Toni Kroos did so successfully in the first half of the first leg of Liverpool’s Champions League defeat to Real Madrid. Liverpool at their best are able to guard against that problem with their pressing: the trouble against Madrid was less the space Kroos was targeting than the fact he had several seconds to measure his pass.
Given the lack of time available to international managers, and given the Euros are likely to be characterised by exhausted players – something acknowledged by the increase in squad size – Southgate may perhaps reason he cannot achieve the required level of pressing and so Alexander-Arnold is not worth the gamble when there are three high-quality, less-attacking right-backs available.