Perhaps what's needed is for people to share their experiences of getting a counsellor/psychologist with appropriate expertise.
My own impression is that specialist provision is extremely patchy, and that the people who need assistance most will often find it hardest to access it. If a GP is a first point of contact, will they be helpful? It might be that if a partner who is ASD is holding down a decent job and the household is outwardly stable, a doctor is not going to regard a partner's unhappiness as pressing. The most the partner could hope for is a number sessions with the practice counsellor.
Or someone whose marriage is unhappy might contact Relate. I'm assuming the Relate training does not currently cover issues in ASD/NT relationships is any depth, if at all.
Deciding to go the private route is an option for some. However many people have posted here about finance being a difficult area of communication in the relationship. Given that private counselling for individuals starts at around 40 a session, how many couples are going to be able to agree - and have the resources - to invest in a series of sessions. (I'm assuming that the rate for couples counselling may be considerably higher.) If the counsellor feels that it would be useful to see the partners over quite a long period we are talking about four figure sums. (Less money for spouses to pursue their special interest, less money for bills, petrol, essential items.) Plus there's possible need to pay for babysitting, the cost of getting to sessions if the counsellor doesn't live five minutes walk away.
It's an almost entirely unregulated profession with a wide variety of approaches. Most counsellors will claim to be able to work with a huge range of issues. However it may just be that they're interested in these topics and have covered them briefly in training. Does this mean that people who are stressed and vulnerable should be prepared to open up their soul to a private practitioner who may have good intentions, but very little relevant experience?