Answer
Reinstalling RSAT after upgrading the build of Windows 10
Indeed, there is such a problem. Each time when the Windows 10 build is upgraded, the RSAT files are deleted (the dnsmgmt.msc, gpmc.msc, dsa.msc, etc. removed from folder the %SystemRoot%\system32\). To restore administrative tools, you need to manually download and install the latest version of RSAT from https://www.microsoft.com/en-us/download/details.aspx?id=45520.This is by design restriction and somehow bypass it will not succeed. You always need to install the latest version of RSAT for your W10 build. 
As you can see, the current version of RSAT at the moment is 1803 1.0 (May 2, 2018),
Microsoft requires that after upgrading the system, you must always delete the old version of RSAT and install the current version of the remote administration tools for your Windows 10 release (different versions of RSAT cannot be installed on the computer at the same time).
Can’t Uninstall RSAT (KB2693643) on Windows 10
In some cases, the old version of RSAT during the upgrade is uninstalled incorrectly (only a part of the snap-ins disappear). In this case, you must uninstall the update KB2693643 (this update contains the RSAT tools). However, if you try to remove the update via the Control Panel, you may receive an error:
An error has occurred. Not all the updates were successfully uninstalled
If you try to uninstall the update using WUSA from the command prompt (wusa /uninstall /kb:2693643), another error occurs:
Installer encountered an error: 0x8007005. Access is denied.
If you analyze the log file c:\windows\logs\cbs\cbs.log, you can find that the uninstall error is due to the fact that the installer can’t delete the registry key: HKLM\SOFTWARE\Microsoft\Fusion\PublisherPolicy\Default\ v4.0_Policy.3.1.Microsoft.UpdateServices.Administration__31bf3856ad364e35.
This key must be removed manually:
Get-Item HKLM:\Software\Microsoft\Fusion\PublisherPolicy\Default\v4.0_Policy.3.1.Microsoft.UpdateServices.Administration__31bf3856ad364e35\1\4.0.0.0 | Remove-Item
Then try again to remove the RSAT update using WUSA or DISM:
dism /online /remove-package /packagename:Microsoft-Windows-RemoteServerAdministrationTools-Client-Package-TopLevel~31bf3856ad364e35~amd64~~10.0.16299.2
You can get the full name of the RSAT package using the command:
DISM /Online /Get-Packages | find "RemoteServerAdministrationTools"
The update KB2693643 should be deleted successfully. After rebooting, you can install a new version of RSAT.
Missing DNS manage console in RSAT after Windows 10 upgrade
There was another problem: after reinstalling RSAT on the computer, the DNS management console (dnsmgmt.msc) is missing. To fix the problem, you can copy the files dnsmgmt.msc, dnsmgr.dll, DNSmgr.dll.mui from the another Windows 10 host and register the library:
regsvr32 c:\windows\system32\dnsmgr.dll
Also you can install WS_1803 or WS2016 RSAT instead of WS_1709 RSAT.
In addition, the Microsoft website has an official KB article 4055558 (DNS manager console missing for RSAT client on Windows 10). The article states that to fix the problem on Windows 10 x64 you need to create two files:
installx64.bat
@echo off
md ex
expand -f:* WindowsTH-RSAT_WS_1709-x64.msu ex\
cd ex
md ex
copy ..\unattend_x64.xml ex\
expand -f:* WindowsTH-KB2693643-x64.cab ex\
cd ex
dism /online /apply-unattend="unattend_x64.xml"
cd ..\
dism /online /Add-Package /PackagePath:"WindowsTH-KB2693643-x64.cab"
cd ..\
rmdir ex /s /q
unattend_x64.xml
<?xml version="1.0" encoding="UTF-8"?> <unattend xmlns="urn:schemas-microsoft-com:setup" description="Auto unattend" author="pkgmgr.exe"> <servicing> <package action="stage"> <assemblyIdentity buildType="release" language="neutral" name="Microsoft-Windows-RemoteServerAdministrationTools-Client-Package-TopLevel" processorArchitecture="amd64" publicKeyToken="31bf3856ad364e35" version="10.0.16299.2"/> <source location="." permanence="temporary"/> </package> </servicing> </unattend>
You need to put the MSU file of RSAT in to the directory with the files and run the file installx64.bat. As a result, RSAT is resets and the DNS management console appears.