Q.See question above. I did some research on Sefarim  on my last Shaila and found that many recommend  not to use a water faucet that has a single spout. Is that because of the reason you mentioned above?
A. An excellent description of this Shaila and the issues involved is given by Rav Tzvi Goldberg from Star-K as follows; On a one-handled faucet, both hot and cold water are controlled by one handle.  Generally, it works as follows:  When turning on the faucet with the handle set in the middle position, there will be an even mixture of hot and cold water.  As the handle is turned towards the right, a valve closes off the hot water and the water will be mostly cold; if the handle is pushed all the way toward the right, the water will be only cold.  In this case, to avoid Shabbos transgressions, one would use the one-handled faucet with the handle turned towards the far-right position.
Nevertheless, this handle poses a Shabbos challenge since one always has to remember to first push the handle lever towards the far right before turning on the faucet.  This is not how it is normally done, as usually someone who wants cold water turns on the faucet with the handle facing the middle and then pushes it over to the right.  Force of habit might cause one to do this on Shabbos.  Also, a guest or child may not realize that this is an issue at all, and may unwittingly transgress the issur of bishul on Shabbos!  An additional concern is that some one-handled faucets do not have a way of turning “all the way to the right.”  They turn 360o around and around.  A person can easily misjudge where to turn the handle.
Due to the above it is highly recommended to avoid having and using single spout faucets during Shabbos.
Horav Shlomo Miller’s Shlit’a opinion is similar.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller, Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit’a