Sure, but with fixed hardware resources you risk the site going down with traffic spikes like this, with AWS you have access to calculatorless options that can easily scale to handle increased request volume.
If you use an an alt-CaaS you'll won't benefit from Infinidash integration, but then again you won't have the Infinidash configuration learning curve to deal with so it could still end up a net positive.
Actually, HIPAA auditors would probably love a webserver running on a Casio since the hardware can be closely vetted and won't randomly change.