Big clients tend to be very slow at signing contracts because their legals would examine every word and will keep asking you to revise the contract. Furtheremore, real big clients tend to be slow at adopting the techology they just bought, so you may not get feedback quick enough to improve your product. Big clients are more likely to argue for discount as they would use "I am big name" as leverage.

This, and sales concentration is a real risk as well. If you have few big customers and even one of them churns, the impact this will have on you is certainly going to be material.

Yes, the strategy for big client is to lock them in for long engagement (like a 3-YR term). Throw in some nice support package, longer trial period, whatever. Since big customers often take months to fully use a product (6-12 months is very common), I wouldn't worry about "oh now I got big name, I need more infrastructure, more money to pay my cloud vendor." It won't for 6-12 months and you probably can keep all the pennies from the big client monthly. If you get a downpayment (say 1-year for a 3-yr term), you get ammunition to grow your team and get more smaller customers.

That is true for consulting and manual/in-person kind of service. However with SaaS the automation is crucial to service the masses.