Where static wins
Speed, because pages are ready to serve. Security, because there is no login page, database or plugins to attack. Running costs, because hosting is simple. Peace of mind, because there is nothing to update and nothing to break.
Where WordPress wins
When you or your team edit the site every day, run a large blog, or need memberships, many logins or complex plugins. Editing in WordPress is quick and familiar.
The middle ground
A lot of business sites change a few times a year. Those do not need a content system running all day. A static site, plus someone who looks after the changes, usually serves them better and costs less to run.
Shops
A small shop can be static with a proper back office behind it. We built that for ECRU Studios, with stock, orders, invoices and checkout handled by software made for them. A very large catalogue changing all day may be better on a platform made for it.
How to decide
Ask three questions. How often does the site really change? How much has it cost you in updates, rescues and licences? How would a day offline hurt you? If it changes rarely and downtime hurts, static is probably right.
Questions
Is a static site less flexible?
It is more fixed, which is the point. If you need something dynamic, such as bookings or orders, it can be built in alongside the static pages.
Is it good for search?
Fast, clean pages are a good foundation. Rankings still depend on your content and your competition, and nobody can promise a position.