Delving back into my previous history as an assistant inspector of what then was then the "Inland Revenue", the "Wholly, necessary and exclusively" stipulation has been the bedrock of expense claims for many decades.
The distinction that needs to be made here is that of employment. If you were already employed with an employer that required you to undertake that training at your own expense, then of course (assuming the wholly, necessary and exclusively criteria was met) the expense would normally be allowable. The revenue has never considered specific training within employment as a benefit in kind (bik) so that argument is redundant.
If a potential employers offer of employment is conditional on you satisfying qualifying criteria (in this case a type rating) then that is an expense that is incurred in order to put you in a position to undertake said employment and therefore doesn't satisfy the "wholly, necessary and exclusively" criteria.
In the nigh on 40 years since I waved goodbye to HMRC's predecessor, I have seen airlines move from an era where they all paid for training, to one where they got a bit fed up with paying for that training only to watch people avail themselves of it and then leave. This was countered by introducing "bonding" schemes. A few people failed to satisfy these "bonds" and pursuing them simply became added expense and inconvenience. The next stage in that evolution became "bonds" where the prospective employee needed to shoulder the financial burden up front in order to transfer the burden of risk.
Nowadays the majority of airlines seem to employ some variation of this strategy whereby unless you have the qualifications they require (specifically a type rating) prior to an offer of employment, the cost of obtaining that rating falls upon your shoulders. Unless you were self employed when it may be possible to claim this as an input cost, it simply falls into the category of any other "loan" or expense that puts you in a position to undertake said employment.
Not saying I agree with this, but that is a very simple explanation of the distinction and a very potted history of why we are where we are.