I have over 10,000 paying customers. I receive maybe 5 emails per day. There was never a time when I received much more than 10. I have three explanations for this:
1. I have a really good FAQ that answers almost any question. On my contact form, I urge people to read the damn FAQ. If they still send me an email, I usually reply with a specific link to the FAQ item. If a question comes up a couple times, I add it to the FAQ.
2. Since my product isn't free (and not cheap compared to a 0.99 one-time-fee app), there's a lot of self-selection. I don't have to support freeloaders with their stupid questions. If people pay for something, it seems to help to reduce the support burden.
3. I wonder if this is a mentality thing and Germans are more likely to help themselves through reading FAQ than others who rather send an email like "yo, shit is broken, fix asap". Most emails I receive read a lot more like a letter and not this one-line blurp bullshit some have to deal with.
In essence: Build a product with a somewhat sophisticated target group. They are more likely to pay, more likely to help themselves by reading FAQ and more likely to send no stupid emails.
As a B2C SaaS product it actually seems to be relatively cheap: 10,000+ paying users and 370,000€ in yearly revenue points to around 2.99€ / month and 29.99€ / year subscription fees – similar to Instapaper Premium[1].
Also the fact that you don't sell at discount likely filters out the bulk of self-entitled users that tend to stress support with trivia.
And your summary is 100% spot on - catering to a more savvy audience and aggressively culling other users is a good way to keep support manageable (and even pleasant!)
Another thing probably is, that a subscription price of a niche product can be considerably higher than of a mainstream one?
For a single person, it must be much easier to support 1,000 users paying something like $25 / month than 5,000 users paying $5 / month.