For me, the biggest asset of Search Console is that it's a free product! You don't need to pay extra to obtain data that other tools will give you. If you want to know which keywords your visitors are using to find you, then look no further. Google Search Console is also a …
If you notice your site is taking a long time to load, then you should first use PageSpeed Insights to see what can quickly be optimized (also check your file sizes, hosting server, NGINX and other common sources of slow speed, too.) And, if you've notice gradually fewer Organic Search visits, PageSpeed Insights might be able to help. As Google is reducing the prevalence of slow sites, you could be losing traffic. Speed up your page load times by finding what is blocking renders, slowing down contentful paints, and other critical page speed signals.
Google Search Console is helpful to understand what terms customers search for and click onto your website from. However, it's not helpful if you're looking for deep competitive insight on search terms people are using and how that impacts your website.
More training resources would be an asset. A beginner is given the power to completely destroy a sites search results at the push of a button. Likewise it is a powerful tool to enhance search results also.
An option to take care of multiple versions of the same site simultaneously would be helpful. An option to use the same validation script across all versions and administer them simultaneously would be a time save (i.e. non-www, www, http://, and https:// versions of the same site).
Google Search Console is a simple program that allows organizations to get a solid understanding of the way their site functions and how users land on it. It can be used for making critical business decisions regarding marketing budgets and that within itself is why it deserves a 10.
As with all Google software, your primary source of help is their forums, their knowledge base articles, or whatever tutorials you can find on the web. Often answers on their forums are not straightforward and may not address the actual issue you're experiencing. The KB articles are typically written like instruction manuals - for better or for worse. Tutorials on the web may vary, but the odds are good someone out there had the same questions as you and was kind enough to document their experience.
I think GTmetrix has some feedback that PageSpeed doesn't provide, but Google's tool is easier overall and has a better user experience; also offers compressed images, CSS, and javascript files if that's the case. Also, Google has extensive documentation to help you better understand what can be done to improve your grade.
SEMRush is a supplementary tool we use to provide competitive analysis. While it does, or should, provide the same data that Search Console does, but I only fully trust Search Console when it comes to basic performance in Google for the sites we develop and own. SEMRush, and other products like it, does provide much more in-depth insights that can help drive business decisions, including site performance on other search engines, along putting organic and paid search performance in one spot. However, SEMRush costs money while Search Console is free.
Given that this is a free tool, the return on investment has been particularly high - we've identified and addressed a few site issues that could have meant a reduction in search traffic.
Our organic search traffic has been on the rise in part due to the insights gained from the search traffic analytics provided within the console.