WooCommerce runs perfectly well on shared hosting for the great majority of shops. It is, however, considerably heavier than an ordinary WordPress site, and it is worth understanding why so you can tune it rather than simply outgrow it.
Why it is heavier
A normal WordPress page can be built once and served to everybody. A shop cannot: the basket, the account pages and the checkout are different for every visitor, so those pages are built from scratch every time. WooCommerce also adds tables, runs background jobs, and keeps a session for every visitor who touches the basket.
What that means in practice
- Caching still matters enormously – but it must be configured correctly, because some pages must never be cached. See Caching WooCommerce correctly.
- The database grows faster than on a normal site, particularly sessions and scheduled actions.
- Admin work is expensive. Bulk editing products, running reports and importing stock are heavy operations. Do them at quiet times.
The practical limits
Shops with a few thousand products and ordinary traffic are entirely at home on shared hosting. The things that push a shop past it are not usually catalogue size but sustained concurrent checkout traffic, very large imports running constantly, or a plugin doing something expensive on every page load.
Before assuming you need more
Check Resource Usage in cPanel to see which limit you are actually reaching, and look at the cause. In our experience the majority of "we have outgrown the hosting" cases turn out to be a missing cache, an uncontrolled bot, or one badly behaved plugin.