Can’t believe there’s still no “official” answer here. Post #9 says Eufy support says the resistor is required. Post #11 says (correctly) that the install manual only suggests shorting your legacy chime out of the circuit. Post #26 says Eufy claims no resistor is necessary.
Post #15 says that without the resistor, output from the transformer isn’t stable. Post #18 says his 40VA transformer is getting hot, due to underloading.
I think the confusion must be coming from the various combinations of legacy chime / no legacy chime, and wired Eufy / battery Eufy.
The wired Eufy page says: “the doorbell requires you bypass the existing doorbell chime. It’s as simple as connecting a jumper on the chime.” The battery Eufy page says: “Compatible with mechanical chime (not digital chime)”. This seems like it implies a fundamental difference in the power requirements between the two models.
I can only speak to the wired Eufy, which is what I have. But I don’t see why jumpering the legacy chime would require a resistor. If you look at the Eufy install manual, jumpering the chime would create a direct short between the transformer contacts. (As explained in post #27.) But this is not the case when the Eufy replaces the original doorbell button. Unless I’m missing something, the jumper essentially simplifies the entire circuit to two unbroken wires. And at the “button end”, there is no longer a simple contact switch - there’s a device (the Eufy) that accepts 24VAC. So no short circuit, unless the Eufy creates one - which it won’t, since it’s not expecting a legacy chime.
This same argument holds in the case where there’s no legacy chime at all. The wired Eufy isn’t compatible with a legacy chime, so presumably it’s “expecting” a direct connection to the transformer, with no additional load.
But the battery Eufy claims to be compatible with a legacy chime. So maybe it’s “expecting” that load - whether it comes from the legacy chime, or the resistor that mimics the legacy load. (Though the manual doesn’t say a resistor is required.) If the doorbell’s internals essentially mimic a legacy contact switch when the button is pressed, creating the short-circuit situation described above, then a resistor makes sense to me if there’s no legacy chime. (Note that if you google around, you’ll find a similar mess of answers for the Ring doorbell… Different models do/don’t require resistors.)
TL/DR: My electrical engineering degree is super dusty, but if someone knows a reason why the wired Eufy would require a resistor, when it’s expecting no load on the wire, please feel free to correct me.
(p.s. - my wired Eufy has been working well enough for 2.5 years with the 24V / 500mA transformer I linked in post #10. No legacy chime, no jumper, just wired right into the transformer. I haven’t checked the transformer for heat, though.)