What exactly is the issue/problem that you're trying to convey?
One can use any search solution, from the most basic to the most advanced one, with any server-side technology.
Even if your hosting provider doesn't allow you to run some technology stack, there are hosted search solutions with APIs you can use.
And it's not like any but the most basic of sites should not use at least a VPS anyway.
What exactly is the issue/problem that you're trying to convey?
One can use any search solution, from the most basic to the most advanced one, with any server-side technology.
Even if your hosting provider doesn't allow you to run some technology stack, there are hosted search solutions with APIs you can use.
And it's not like any but the most basic of sites should not use at least a VPS anyway.