Dameware Mini Remote Control. SWEET little program. Allows access to the 'console' session, the login screen, the boot process (if you use Intel AMT) and also allows to switch to existing RDP sessions as well.
Multiple connection methods: MRC (their ridiculously fast proprietary solution) RDP, VNC, intel AMT (vPro). Multiple authentication methods (NTLM passthrough/manual entry, custom credentials). I've used it for years, well worth the price.. let me know if you have any questions.
Also, for what it's worth, mstsc /admin definitely DOES connect you to the console session, but the console session is NOT the login screen.
However, if you are intending to connect to Session 0 (which is not the console session), simply set HKLM\SYSTEM\CurrentControlSet\Control\Windows\NoInteractiveServices=0 and then start the Interactive Services Detection service. If a service (or any other process) is running interactively in session 0, a window will pop up advising you and allowing to switch to session 0 and interact with the process
To more thoroughly answer the question:
There is no 'more native' (as in built-in) solution that will allow you to control the 'physical desktop' of the server. RDP will only allow access to the logged-in 'console' SESSION. It in no way provides access to the 'physical desktop' of the server. RDP is not a display 'hooking' technology, like VNC, etc, but it works fine for most purposes. If, like me, a person finds themselves regularly needing access to the 'physical desktop' of machines, a third-party solution is the only choice.
I should add, this is why there are MANY third-party remote access tools offered by reputable vendors. Intelliadmin, Radmin are a couple others that immediately come to mind.
Since I'm getting bashed I feel like I should add some more info... Most remote access solutions require (or at least install by default) a client executable and/or driver that runs at ALL TIMES on the remote host. Dameware does not. It has a friendly interface that allows an administrator to push and install/start/stop/uninstall the remote host service on-demand to the machine by RPC/Remote Services Administration. It can automatically install/start the service when connecting and then stop/uninstall the service when disconnecting. This negates the 'driver hack' attack vector mentioned in a comment below. This is how I have my systems configured. And of course only a user with proper admin credentials can make this happen.
P.s. I am in no way connected to this software vendor (now owned by SolarWinds).
Also, I'd argue that from another perspective on the word 'native', VNC, or even better Intel AMT or other similar hardware-based display-hooking technologies (HP iLO, Lantronix Spider KVM, etc) are about as 'native' as you can get.