Lowering pit lane speed limits to 60kph will not make it that much safer, it will have an effect for sure but not so much as to make pit road safe.
If you want a safer pit lane you first need to identify the hazards. Speed itself isn't a hazard it is merely a condition something is at. F1 racing mainly uses lower order controls to maintain safety, they being engineering, administration (rules, regs) and PPE. Lower pit lane speeds may slightly lower consequences but it does nothing for exposure. The risk will still be very high.
Rarely are the higher order controls used, elimination, substitution/isolation. Examples of these however are the advent of barriers to isolate the racing from the public, banning of materials, limitations on the tech regs to eliminate other hazards.
If they want a safe pit lane remove that hazard, no pit stops, if they want pit stops change the rules where pit crews are not near any car on pit entry, you could go further and isolate each team from each other. The later is not practicable, so removing pit stops would eliminate the hazard. Lowering speeds will make no real change to a worst case outcome.
The main reason there are very few incidents now in pit lane is the robust administrative controls, training, rules, etc. Racing however is a window where these controls can fail because of pressure and reduced timelines for thinking something through. Reducing speed may allow more time to think, but the nature of racing will eat up any additional time by allowing the teams to add more complex decision cycles to get a racing advantage and probably negate the control.
I think the FIA and the teams have already been through their risk assessment and mitigation routines. There is, after all, already a speed limit in the pit-lane in addition to the regulations regarding what work may be done and when, the restriction on personnel allowed in the area, the PPE, etc. In cost-benefit terms, reducing the speed limit seems to be a cheap and easily implemented action. Without doing our own analysis we don't know what other options are practical and effective. It would be interesting to know whether Whiting has any other plans to reduce the risks in the pit lane. If he hasn't then he is effectively saying that he (and/or the FIA) considers the current level of risk to be acceptable. If he has, then maybe the teams' proposal of reducing the speed limit was their counter to FIA plans that involved extra costs to the teams?
And the softly softly health and safety approach has gotten the world into the state its in. People are afraid of their own shadow now. What happened to survival of the fittest?
Logically, it led to the current situation that you appear to be unhappy with.