I used to be on a board of trustees for a charity and I agree that it was not my responsibility to be available to staff, just as a director on a company board is not usually available to staff either. We did go to events though.

I think the arrangement being suggested is quite unusual, but I don’t think there is anything wrong with it if done the right way. Could it be reframed as trustees mentoring staff?

I am a deputy chair of trustees and would say that what is being proposed is out side the remit of a trustee. However i am involved in yearly appraisals which i enjoy and i do this with the manager. We were a trustee board too divorced from what was happening and it was only a crisis that highlighted this so trustees are now more involved. At all trustee meetings we now have presentations from staff to update us and we attend social events as asked. I would not have time to buddy up but having trustees who are responsible for certain things such as safeguarding etc is good practice.

It depends a bit on your governing document but my concern with buddying in this way is that rather than acting in the trusts overall interest they could be overely influenced by their buddys perspective. If their buddy employee did need to complain, i think they would have to have their complaint heard by a different trustee to the buddy.
I personally think trustees are better having a focus 'job' like safeguarding or staff wellbeing - than being paired with an individual but I couldnt say outright they were doing something wrong. It depends how operational they are supposed to be.

I think this is madness, it means you would be having to negotiate with two people per employee about their development.

The whole point of trustees is that they are supposed to be slightly seperate to give that overview. This to me looks like it is getting too close for them to be able to have that overview of the charity.

I'd ask them to park it for the time being, to see if the changes that you have made are working and bring it in with further thought if it is needed in the future. I wouldn't mention this to the team at all if it hasn't already been broached.

What i will add is that we have an amazing long term manager who was super good, we let her get on with it which made us unconsciously step back, but the same can happen with a poor manager and the team feel unheard and need more trustee involvement. It sounds like this has happened in your organisation.

I am a trustee for a small charity. We are semi-formally buddied up with the paid staff; based on the individual trustees skills base (which is varied). I work in education so act as a sounding board/source of advice for the education officer for example. Another trustee has a background in media has the same role for helping out the staff member producing promotional material. This was welcomed by the charity director and we are positively encouraged to 'touch base' with our buddies. We also have a face to face meet up once a year which is great. We have sub-committees that meet regularly that comprise trustees and staff members which allows the charity to draw on a wealth of experience and contacts in strategic planning. It works well for us!

I think the risk with this is that the trustees can get too operational rather than operate at their proper level but, in smaller charities, having a set up like @fuckweasel suggests can work well as otherwise individuals can feel quite isolated, not know where to turn for support and, importantly, if they're rubbish at their job, it can take a while for anyone to notice.