PowerShell Core intentionally does not replace the built-in PowerShell:

Does PowerShell Core affect my Windows PowerShell installation?

Nope! PowerShell Core is completely side-by-side with Windows PowerShell. In fact, an awesome feature of PowerShell Core is that you can test new versions without affecting existing workloads. Whether it’s installed via an MSI or installed portably from the ZIP package, your Windows PowerShell installation is not affected by PowerShell Core.

Since PS Core does have backwards-compatibility-breaking changes, this is probably not a good idea just yet. You'll find some administrative modules will not work in PowerShell Core.

Microsoft is still working on a roadmap for bundling PowerShell Core into Windows by default. It is entirely possible that the older PowerShell 5.1 is still included for backwards compatibility - in much the same way IE is still included despite Edge being the default.

If your goal is just that launching powershell.exe will launch Core, you can place the PS Core folder earlier in the PATH so it is discovered first. Note that this could break scripts that need anything PS Core does not support.