Aye. The Sporting Director, Head of Recruitment and
possibly the Chief Executive or Club President (if this person possesses the breadth of knowledge to have a say in such matters, like José Ángel Sánchez at Real Madrid or Uli Hoeneß at Bayern Munich in the past) should be the ones driving our transfer operations, after carefully considering the opinions of experts in the scouting and analytical department of course. And they should be expected to always act in the best interest of the club, particularly with the medium to long term health of the institution in mind, which calls for consistency of vision and decision-making (and sometimes, sacrificing the short term), with good working practises and senstivity (with regard to the unavoidable human element) creating a snowball effect and ensuring the optimization of their collaboration.
A lot can go wrong if a contemporary Head Coach is allowed to weild excessive influence in non-coaching departments, particularly at a club that hasn't the foggiest idea about constructing a robust, competitive decision-making hiearchy (like Manchester United). If I recall correctly, the average Premier League based Head Coach has a lifespan of a bit less than 1½ years — they might be good coaches and trainers, but not necessarily the best talent identifiers (which is an art form, even in the age of big data), and that would make them fundamentally unsuited to overt transfer-related intrusion. And when push comes to shove, they will act in self-interest and make short-termist decisions to protect their own jobs (which might or might not be in alignment with the interests of the club itself), while recklessly stockpiling on personal favorites that would be subpar, if not redundant, under their successor (particularly if their principles of football and tactical leaning are divergent), which is just precious money down the drain.
CIES Football Observatory: Demo-economic analysis of player transfers (2014-2023)
Manchester United needs to learn from its multitude of mistakes in the post-Ferguson era, and should be structured so that the club can smoothly navigate semi-regular change at the Head Coaching position (this happened at most of the successful clubs of the last 10-20 years...including the trio of Real Madrid, Bayern Munich and Barcelona). That needs to be our default setting. And while we shouldn't be inherently midstrusting of Head Coaches, we should be strict with the near-absolute bifurcation of responsiblities, instead of entertaining their whims and fancies and hastily handing them the keys to the entire castle (in the hopes that they will turn out to be messianic figures, following in the footsetps of Busby and Ferguson). Slight accomodations should only be made for exceptional ones who have clearly evidenced talent-assessment pedigree (ideally at Manchester United, just to make sure they work well with the ideals and structural underpinnings that are specific to this club). For the most part, Head Coaches should stick to training and improving the group of players they have at the disposal, as opposed to micromanaging other departments.