WordPress Client – expensive hosting

Hi all,
I have a query that I am really looking for to get a second opinion from you.

We have a client who recently migrated to us … we are a web agency.

For hosting, we used a couple of shared hosting providers, as well as WPEngine for larger WordPress sites, and a separate host for large Magento sites.

The client site is a WordPress site, which in the initial view before the migration showed around 30,000 visits per month.

After migrating to WP Engine, after a few weeks, we received a call from the WP Engine support people telling us that the site literally consumes bandwidth. It is actually receiving about 100k visits per month in current estimates. After much discussion, it seems that this will mean switching to a plan that costs $ 115 per month in the short term … and a package of $ 290 per month in the medium and long term.

Understandably, the client is quite upset about this … since they have been used to paying a few hundred dollars per year so far … although on a totally inadequate server.

So I just need a second opinion really … The customers' site is small in size … but very high in traffic (as above). The client has asked us to find an option that DOES NOT base its prices on server utilization or bandwidth … and it is not as expensive as several hundred dollars a month.

I'm struggling a bit to find an option that we can work with … that I know will not fall every day.

Can anyone suggest an economical but stable platform for a WordPress site with a lot of traffic … that does not change prices according to usage, but is it able to remain stable during busy periods?

Thanks for any advice you can offer.