Hi David and welcome to the forum,
You're absolutely right, dropshipping margins are tight at the very best of times, people tend to use that platform as a cheap way into the market because of low to no cashflow. Those with cashflow tend to look to wholesale avenues to secure better margins on products.
That said, is it possible to make money from drop shipping? Well that's kind of an open ended question, really. Probably depends on how you quantify the term "make money" Those that are successful at making most from dropshipping tend to use the saturation method, that is list a load of products. Of course the theory being that the more you have listed, the more chances you have of getting multiple sales.
That strategy can work, but it also has it's pitfalls as well. You still need to ensure your products are well placed in the market, that is competively priced, your branding and service is on point and you've essentially ticked all the boxes to give yourself the best chances of making sales. Then on top of that, you also have to be aware of listing fees, because on a site such as an eBay, you're paying to list if a product sells or not.
On your own website, that's not an issue, so you can stock your own website to the ceiling with dropshipped products and that's where I personally think dropshipping works best. Of course then you need to drive the traffic to your website or no matter how well it's stocked, you're not going to be making many sales.