Why can't quantum tunnelling carry energy or information faster than light?

A few experimenters have at one time or another claimed that quantum tunnelling allows the transfer of information or energy at superluminal speeds.

One was the idea that music was carried across a Josephson junction faster than light, because the electrons carrying the signal tunnelled instantaneously across the junction.

Another was that photosynthesis might transfer energy from the photon capture site to the chemical reaction site superluminally, because the exciton tunnels (or follows a daisy-chain of tunnels) from the one to the other.

Timing measurements were produced in support of these claims of superluminarity (or rather, the claims were drawn from the results presented).

Further studies have supported the superluminality of tunnelling (see Natalie Wolchover; "Quantum Tunnels Show How Particles Can Break the Speed of Light", Quanta Magazine, October 20, 2020). But the carrying of information or energy with that is far less clear.

Is there a sound theoretical reason for rejecting such ideas of superluminarity in quantum tunnelling? For example entanglement can lead to superluminal or even (in theory) retrocausal sequences, but this cannot be used to carry energy or information. If this also applies to tunnelling, then how come?