“Do you think people with old ‘silver’ fillings should have them removed and replaced by more up-to-date materials?”
Although there is no conclusive research showing that silver (aka 'amalgam') fillings are harmful to your health, other problems can occur. The most common problem is not cavities or leakage, but cracks.
Often cracks are asymptomatic and can be monitored without treatment. However they can grow larger over time and a lack of pain can hide their slow propagation. If the crack eventually reaches the nerve of the tooth, a root canal treatment will be necessary to fix it.
Or there may be no symptoms at all for many years and then, all of a sudden, the side of the tooth can break off completely (and sometimes without any pain!). When this happens, the tooth might be reparable with a crown (aka 'cap').
So the answer depends on whether you prefer to be proactive or reactive. Most folks who have had silver fillings for many decades with no problems at all prefer to avoid treatment if possible. But if you've ever had to repair one of your teeth because it broke like this, you'll likely be interested in protecting your other teeth from the same problems.
It also depends on the size of the silver fillings. Replacement of small silver fillings is very predictable and can be done with white fillings. However, replacing larger ones often requires crowns ('caps'), and sometimes even root canal treatment.