Does this not mean that we should stop using cermaic capacitors of this type?

Four parameters that make ceramic capacitors desirable:

1. Low ESR
2. Low ESL
3. Small size, especially surface mount.
4. Very inexpensive

Or is there a way to mitigate this problem?

So if, by design, the capacitor volage is constant, then there is no reason not to use a ceramic. If 10\$\mu\$F is desired , but at the operating voltage the capacitor has 50% of its value, then use a 20 \$\mu\$F value or two 10\$\mu\$F in parallel.

Does this not mean that we should stop using cermaic capacitors of this type?

Four parameters that make ceramic capacitors desirable:

1. Low ESR
2. Low ESL
3. Small size, especially surface mount.
4. Very inexpensive

Or is there a way to mitigate this problem?

So if, by design, the capacitor volage is constant, then there is no reason not to use a ceramic. If 10\$\mu\$F is desired , but at the operating voltage the capacitor has 50% of its value, then use a 20 \$\mu\$F value or two 10\$\mu\$F in parallel.

Edit:

The variation of capacitance with voltages is more severe with smaller volumes. Example 0402 exhibits extreme dependance while 1206 is mild. If the board real estate allows, then the larger volume capacitor may be preferred.