I use a mirrorless interchangeable lens camera. These do not have that problem. I do not have a touch screen on mine although some do. So I flip the screen up, bend my knees and look down on the screen and then press the shutter button (could use a remote). Bridge cameras are generally mirrorless in design. They do not have optical viewfinders (or mirrors which have to be lifted for live view) so getting a modern mirrorless camera with a good electronic viewfinder and refresh rate (not much lag) can be important.
Bridge cameras (have one fixed lens) and interchangeable lens mirrorless cameras shoot in a permanent live view for want of a better way of putting it. They then display the view either on the back panel or into an electronic viewfinder (if it has one). Being designed to shoot this way they don't suffer from the mirror and shutter problems of your Nikon in live view.
I'll not go back to DSLR's for the type of shooting I do. Both systems have pros and cons and both systems can take great pics.
You can spend £3000 (or much more) on a mirrorless these days of course you can also buy cheap ones.
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Or More !!!!
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Or even more !!!!
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