Just for interest, many engines of recent times have used roller finger followers with hydraulic pedestals. There are three principal reasons for this arrangement. First the consistent valve event control is very useful for emission control with the ever tighter regulations, second it is a convenient way to introduce a roller follower (the cam lobe operates a roller rather than sliding on a solid surface) which substantially reduces frictional losses especially at lower speeds, and hence fuel efficiency, and third it is essentially maintenance free and reliable.
One other comment regarding clearances/noise. Cam profiles have a "ramp" at each end (opening and closing) which is usually of what is known as a "constant velocity" design, the velocity being defined as lift per degree of rotation, cam profile data is related back to angle round the cam so actual engine speed has to be considered to get true velocity in absolute terms.
Depending on the design (rocker/finger/direct bucket/pushrod etc) the ramp height will allow for a working clearance to avoid it going tight and keeping the valve partially open and allowing for thermal expansion. This also means that providing the clearance is taken up while still on the ramp, the actual impact ("jerk") which causes the noise remains essentially the same regardless of what the clearance is set at. The ramp rates are empirically set as a compromise between length of ramp and thus uncertainty of when it actually starts to open, the impacts and hence noise and wear especially when the valve is seating.
Hydraulic elements used in valve lash adjustment actually operate with a certain amount of compliance, some slight compression occurs as they are loaded up when the valve starts to lift, so a ramp is still required to accommodate this. There is also a small amount of "leakdown" during the lift so the closing ramp is invariably slightly higher than the opening side.
https://www.tildentechnologies.com/Cams/CamDesign.htmlOver the years I've done quite a bit of valve train development on a variety of engine types during my career. The instrumentation side of this is quite challenging sometimes but very satisfying when it works.