Charcoal, 10 bytes

ＦＡＦι⊞υιＩ‽υ

Try it online! Link is to verbose version of code. Explanation:

ＦＡ

Loop over the input numbers.

Ｆι⊞υι

Push each number that many times to the predefined empty list.

Ｉ‽υ

Output a random number from that list.

8 bytes using the newer version of Charcoal on ATO:

Ｉ‽ΣＥＡＥιι

Attempt This Online! Link is to verbose version of code. Explanation:

    Ａ       Input list
   Ｅ        Map over elements
      ι     Current element
     Ｅ      Map over implicit range
       ι    Outer element
  Σ         Flatten
 ‽          Random element
Ｉ           Cast to string
            Implicitly print

A port of @Arnauld's JavaScript answer in straight succinct Charcoal is only 6 bytes:

Ｉ⌈∨Φθ‽

Try it online! Explanation:

    θ   Input list
   Φ    Filtered by
     ‽  Random coin flip
  ∨     If empty then implicitly use input list
 ⌈      Take the maximum
Ｉ       Cast to string
        Implicitly print

Charcoal, 10 bytes

ＦＡＦι⊞υιＩ‽υ

Try it online! Link is to verbose version of code. Explanation:

ＦＡ

Loop over the input numbers.

Ｆι⊞υι

Push each number that many times to the predefined empty list.

Ｉ‽υ

Output a random number from that list.

8 bytes using the newer version of Charcoal on ATO:

Ｉ‽ΣＥＡＥιι

Attempt This Online! Link is to verbose version of code. Explanation:

    Ａ       Input list
   Ｅ        Map over elements
      ι     Current element
     Ｅ      Map over implicit range
       ι    Outer element
  Σ         Flatten
 ‽          Random element
Ｉ           Cast to string
            Implicitly print

A port of @JoyalMathew's JavaScript answer in straight succinct Charcoal is only 6 bytes:

Ｉ⌈∨Φθ‽

Try it online! Explanation:

    θ   Input list
   Φ    Filtered by
     ‽  Random coin flip
  ∨     If empty then implicitly use input list
 ⌈      Take the maximum
Ｉ       Cast to string
        Implicitly print

Charcoal, 10 bytes

ＦＡＦι⊞υιＩ‽υ

Try it online! Link is to verbose version of code. Explanation:

ＦＡ

Loop over the input numbers.

Ｆι⊞υι

Push each number that many times to the predefined empty list.

Ｉ‽υ

Output a random number from that list.

8 bytes using the newer version of Charcoal on ATO:

Ｉ‽ΣＥＡＥιι

Attempt This Online! Link is to verbose version of code. Explanation:

    Ａ       Input list
   Ｅ        Map over elements
      ι     Current element
     Ｅ      Map over implicit range
       ι    Outer element
  Σ         Flatten
 ‽          Random element
Ｉ           Cast to string
            Implicitly print

Charcoal, 10 bytes

ＦＡＦι⊞υιＩ‽υ

Try it online! Link is to verbose version of code. Explanation:

ＦＡ

Loop over the input numbers.

Ｆι⊞υι

Push each number that many times to the predefined empty list.

Ｉ‽υ

Output a random number from that list.

8 bytes using the newer version of Charcoal on ATO:

Ｉ‽ΣＥＡＥιι

Attempt This Online! Link is to verbose version of code. Explanation:

    Ａ       Input list
   Ｅ        Map over elements
      ι     Current element
     Ｅ      Map over implicit range
       ι    Outer element
  Σ         Flatten
 ‽          Random element
Ｉ           Cast to string
            Implicitly print

A port of @Arnauld's JavaScript answer in straight succinct Charcoal is only 6 bytes:

Ｉ⌈∨Φθ‽

Try it online! Explanation:

    θ   Input list
   Φ    Filtered by
     ‽  Random coin flip
  ∨     If empty then implicitly use input list
 ⌈      Take the maximum
Ｉ       Cast to string
        Implicitly print