Everyone has their thoughts, and plugins definitely slow down a site when used incorrectly, but if you do things right, you'll not have any issues. We moved exclusively to WordPress & WooCommerce design & development a few years ago. I've worked with dozens of carts over the years, but as a company we made the decision to only work in WordPress and WooCommerce, and never looked back.
We manage an online store for a client that runs a "flash sale" every month and generates hundreds of checkouts within 15 minutes - that's significant as these are single items available, it has to calculate shipping and perform checkouts all while others are scrambling to get their one of a kind item. That entire site is WordPress with WooCommerce, and a lot of customizations.
We managed a store that had more than 100,000 products with thousands of visitors and processing hundreds of orders each day - all on WooCommerce without issue.
We've created Vehicles Auction websites with dozens of people bidding and thousands of people viewing - want to see a load spike on a server, watch an auction in the last 2 minutes and then extend by 60 seconds every time a new bid comes in with tens of thousands of dollars at stake.
We currently manage a large online member community built with WordPress, WooCommerce, WooMembers & WooSubscriptions (along with lots of custom code that we've created), and they have hundreds of concurrent members at any given time submitting information, updating calendars, passing business referrals etc.
At the end of the day, it's all about what you know, and what you don't. Large sites on a shared hosting platform can work, provided that the shared hosting platform is optimized to handle such loads. And at the same time, I've seen people crash a Bluehost hosting account installing WordPress and a single plugin that doesn't use any caching.