I think, as someone alluded to earlier, it is not a matter of "...the club doesn't even want to check its assumption at times this season ...". Rather, it has been the case that the club (Le Bris) has not felt able to test whether Neil's level of ability is sufficient for the Premier League. As an earlier poster has said, many games have been competitive right up until the final minute and Le Bris has concluded that he needed the men he feels most confident to deliver on the field. with little chance to speculate on Neil adapting to the level.
I like Dan Neil and believe that he will have a very successful career, but his style of play doesn't fit with how Le Bris wants the team to play.
Who would you drop (or take off mid-game) to accommodate Neil ? Xhaka has become 'undroppable'. Sadiki is not far behind Xhaka in this regard, Le Fee is an entirely different type of midfield player. Diarra, when he returns, is also likely to be a different type and a better player. As a replacement, Geertruida offers better ability, more top level experience and greater adaptability. Rigg, hmmm. It will be interesting to see how the future unfolds. He appears to me to be too lightweight for the rigours of the Premier League, but he clearly has ability.
Neil appears to have concluded that his best option is to sit out his contract and move on in the summer, letting his agent negotiate a hefty signing on fee, in lieu of any transfer fee being incurred, and an improved remuneration package. And good luck to the lad in so doing. He owes the club nothing, having repaid it for the chance he was given, by his on-field contributions in previous seasons. Loyalty means nothing when you are endeavouring to optimise your earnings during a relatively short career.