This post has come up a few times whilst we've been searching for an answer to the "fit to screen by default" Power Bi dashboard problem, so i'll post a possible solution here for anyone who's also stuck as it does not seem like MIcrosoft are going to provide this functionality via the URL params.
Our product VuePilot is used to remotely control and display dashboards and reports on screens in businesses, as such we publish a "Power BI app" that makes displaying Power Bi reports and dashboards on screens very simple.
The Power BI app has an option to "Fit To Screen" for dashboards. This has the effect of essentially triggering that little button once the dashboard page loads and ensures your dashboards fill the screen, instead of only half or so.
You can read more about this option here: https://www.vuepilot.com/support/article/displaying-microsoft-power-bi-dashboards/#fit-to-screen
and some more info about the Power BI app here: https://www.vuepilot.com/features/apps/powerbi
Hopefully that may help anyone else looking for a possible solution
