Am I right in thinking that the more you charge for a service, the higher the cost of support for that customer will beThis is one of those "That certainly feels like it could be true" intuitions which data will disabuse you of in a hurry if you run a SaaS business. Within roughly the same tier of customer -- say, all the publicly available plans on any SaaS whose pricing page you have in your swipe file -- I can virtually guarantee you that customer support costs go down as price goes up. (There's a discontinuity between $500 a month and Enterprise, where support costs may or may not actually go up. Prices go up in a hurry at that discontinuity, though.)
Also: do not price SaaS based on costs. The margins are typically very, very high. Customer support is generally a very low portion of both the costs of the company and the marginal costs for bringing on another customer -- at most SaaS companies I'm familiar with, the #1 cost is engineering salaries and the #1 marginal cost (by a long shot) is costs associated with customer acquisition. (Either advertising spend or marketing/sales salaries.)
With regards to the high churn rate on cheap plans, is it that this is due to the quality of the plans and that it is likely that these customers can find a similar service for free or is it the perceived value to customer is lower because they are only paying a small amount each month?
You're trying to fit a rationalization onto observed behavior, which is dangerous, because customers are frequently irrational. Anecdotally -- and again, social lubricant is a great way to get fun stories from your SaaS peers because darn if we're going to repeat many of these stories while sober [1] -- there's a particular segment of customers who you don't want to be in a relationship with at all, and these customers are disproportionately drawn to your/the market's cheapest offerings. That's not necessarily an indictment of the offering.
[1] I am reusing this joke for comedic effect, as I don't drink, but these are very common topics of discussion at dinners among SaaS entrepreneurs. My favorite anecdote ever:
X: "I get 'My business doesn't make any money, so I can't afford to pay you $20' all the time. What do you say to that?"
Y: "'#$#& you, mine does.'"