Interesting. My own experience with enterprise customer pretty much matches your characterization - departmental sales in a larger enterprise, not sales to the entire enterprise. I sold SaaS project management software into a few pretty big companies, but with specific departments using it (e.g. the graphic design department). Made very few changes for them, other than allowing some generic customizations that would benefit every customer.
A previous business I co-owned on the other hand had the deadly 20% risk (more than 20% of the business tied to one large customer), and that ultimately did not work out well, even though it grew revenue really well for a year or two (big enterprise kept adding seats). It's like a punch to the gut when a very large customer cancels a subscription (in this case it was about $3K monthly revenue). Ouch.
Generally, I'd say small / solo businesses can reasonably offer point solutions for enterprise customers (departmental sales), but will have a much tougher time with "affects the entire enterprise" sales, especially in more mature markets with well-established competitors.
But there are worse ways to make money fast, especially in SaaS, than having large customers giving you thousands per month, as long as you are prepared for the downside risk, and don't hire or grow ahead of the more stable revenue.
I might even make a rule: Safe Revenue vs. 20% Revenue. Only count Safe Revenue in plans for growth, hiring, etc. Just think of 20% Revenue as a windfall.