Standard Security Policy flagging too many emails as "Potential Phishing"

OneTechBeyond, thanks for that note, but admittedly I am a little confused. 
When you say "No EOP/MDO. it's 100% native Microsoft's internal services.", do you mean you are using EOP (Exchange Online Protection) & MDO (Microsoft Defender for Office 365) exclusively, or you're not using them at all? 

It sounds like you're only using EOP & MDO, in which case, follow Ben's recommendations - keep sharing the false positives with us (via admin submissions) and check out the https://aka.ms/emailtech article to get additional insight as to why we marked items as we did (perhaps something is marked due to a user's Blocked sender list, or the sender's service failed DMARC alignment). 

If worse comes to worst, while you cannot adjust the sensitivity of the preset policies, you can create your own policies and adjust as necessary. The Microsoft recommendations for EOP and Defender for Office 365 security settings aticle gives the settings in each policy which align to the default settings (which are pretty low, all things considered), the Standard preset policy, and the Strict preset policy. I'd recommend starting with mirroring the Standard preset policy settings and making adjustments as necessary (based on what you find from the emailtech article), but remember Ben's note that the preset policies are updated automatically to keep up with any changes in recommendations/best practices, but custom policies are not. You would need to review your custom policies occasionally to see how they compare to our recommendations using Configuration Analyzer.