Upgrading to Premium capacity would improve the performance - I wouldn't go as far as saying that it would definitely solve the problem. Whenever you ask for a report export every single page (that you request) needs to be re-rendered. This is a costly operation for regular reports, and even more so for paginated reports that produce pixel perfect results. Having parameters involved may or may not make things worse.
Ideally your data source is in import mode (so you get the guaranteed performance of a Power BI dataset) or your Direct Query data source is optimized for the queries produced by the renderer (including the parameter filters).
There are a lot of moving parts, and most of the complexity is hidden from you behind that innocent little "Export to File" action. So whatever you can do to reduce the computational load will make the process more robust and more performant.
In an ideal world you would not need to do these exports. Yes, I know, rather unlikely to be an option.
