It's very important to have realistic expectations. If you are paying for the cheapest possible hosting on a shared hosting platform, you are sharing resources with other people on the same Plesk / cPanel instance. The risks you sit with, is if one site gets attacked / hacked there will be an impact to your resources. There are mechanisms in place to reduce the blast radius like utilizing things like Cloud Linux with resource fencing, but its not a full proof guarantee.
The only way to guarantee that your site / services run independently on its own, is to get your own private VPS, but then it also means paying more. You get what you pay for. Last thing to mention, the outage you referred to was not planned maintenance that was done in the middle of the day, it was emergency actions performed as there was something wrong on the server that was affected.
I come from a hosting background, and I can tell you people have the most unrealistic expectations with hosting providers sometime. They pay the absolute minimum, but require EXTENSIVE support. From helping customers to setup their email on their phones, tablets, workstations, right through to navigating their way through the Plesk / cPanel dashboard. The amount of times I have had to deal with customers having code issues on their websites, blaming the hosting provider... its incredibly frustrating to explain to a customer that he is paying $10 per month, and that doesn't include having a 24/7 engineer on call to debug his website code because he doesn't have a developer managing it.
Hosting providers will ensure their servers / services are backed up, and outages WILL happen... there are so many moving components behind the control panel you don't see. There are Plesk / cPanel updates, there are customers with bogus code running open relay mail forms, causing entire servers to be blacklisted, and you can only put so many protective measures in place that will do tarpitting, throttling etc. If you absolutely have to have 24/7 high availability, there are products for that at a higher cost.