At least in EU services bought from overseas are subject to reverse charge, i.e. self-assessment of VAT (Article 196 of https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:02... ).
Though note that if you are an EU AWS customer, you are not buying from outside EU, you are buying from Amazon's EU branches regardless of AWS region. If Amazon has a local branch in your country, they charge you VAT as any local company does. Otherwise you buy from an Amazon branch in another EU country, and you again need to self-assess VAT (reverse charge) per Article 196.
Since AWS built a DC in Canada, I’m paying HST on my Route53 expenses, but not on my S3 charges in non-Canadian DCs.
I’m not an HST registrant (small supplier, or if you’re just using services personally), so there’s nothing to self-assess.
Even if self-assessment was required, you get some deferral on paying (unless you have to remit at time of invoice?).
I believe it works differently in EU (i.e. US DCs taxed) as per Article 44 the place of supply of services is the customer's country if the customer has no establishment in the supplier's country.
IBM/Softlayer, Rackspace, Google Cloud, Microsoft and I imagine everyone else large enough to count also does, too.
For Australian businesses, at least, being charged GST isn't a problem - they can claim it as an input and get a tax credit.
Even if you did have to self-assess, better to pay later than right away.