The design of a scatter plot inside Power BI, wherein the X and Y axes can dynamically change with user selection, is best done by making use of field parameters. Such field parameters allow the making of a measure or column option list from users, which dynamically changes the axes in your visual without the use of multiple visuals or convoluted logic.
Here is how it can be done:
Create Field Parameter: Modeling > New Parameter > Fields; select all the numerical fields you want to allow for X-axis usage and repeat for Y-axis. It will create slicers with selectable field names.
Add Parameters For Scatter Plot: Create a scatter plot and assign the X and Y axes to respective field parameter values. This will now be updated based on user-selected fields in the slicers.
Optionally - Theoretical Usability-specific improvement: You may give new parameter values more user-friendly names, and consider using card visuals or tooltips to indicate selected metrics.
It is clean and interactive and only uses Power BI's native support for field parameters to create a seamless user experience when dynamically selecting the axis.