Someone has earlier mentioned wires and banana jacks as the possible cause of meters being limited to 10A.
I’ve checked, how much can some non-specialized wires handle. The burden voltage across a
single wire at 5A
(1)(4):
Original UT70A 116cm, needle: 441mV
Original UT70A 20cm, alligator: 338mV
Shenzhen Market 99cm, needle
(2): 640mV
DT830 66cm, ROTFL quality
(2)(3): 653mV
UniT probes are perhaps not the top quality, but decent enough and I doubt you can get extremely better for kit probes. So even with that we have nearly 1V drop. Extrapolating to 20A: it would be nearly 2V and over 15W in heat. So I guess the hypothesis, that this is a factor, makes sense: a multimeter would have to be supplied with probes designed specifically to handle 20A.
A quick check on Digikey reveals that indeed banana jacks are generally sold in the 5–15A range.
For entertainment alone I’ve checked, how Shenzhen Market alligator wires deal with current. Those which you may hunt down for $0.10/10pcs and treat as expendable. The result is in the attachment.

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(1) I have no meter to measure 10A or a power supply good enough to provide exactly that value.
(2) Added only for completeness, because I had them around.
(3) So bad that the needles have fallen off before the first use.
(4) All measurements at 5A±3%, 60s for letting the current stabilize, 10 samples mean with ±0.5%,1d accuracy.