Barrel charging ports provide a superior user experience: they are easier to use because you can insert the charger at any angle.

Barrel connectors are physically much more robust: they can rotate around their axis without imposing any torsional stress on the device being charged, and the longer lever arm inside the charging device (typically 15 mm) means that flexural stress around other axes creates much less force on the connector. Consequently, they break much less often than pre-C micro-USB connectors. It's too early to tell whether USB-C will improve on its predecessors in this regard, and it may, but it seems unlikely to reach barrel-connector levels of reliability just based on its geometry.

Barrel-connector ports are easier to repair when they break: there are only two wires, and they are quite thick. This is true a fortiori for the cables.

Barrel-connector charger faults are easier to diagnose: either the voltmeter tells you it's outputting 19 volts open circuit (or whatever the rated voltage is), or it's not, or, rarely, it has the correct open-circuit voltage but sags under load, the diagnosis of which requires a voltmeter and a power resistor. Moreover, they are less likely to occur; you are not going to break a bipolar SMPS with static electricity, not even if it is attached to a 5-volt USB cable, but you can easily do that to the CMOS control chips necessary for USB-C voltage negotiation.

Barrel connectors pose less of a security risk: they do not, in most cases, have a data connection at all, and a malicious charger definitely cannot execute a firmware upgrade attack on your device through a barrel connector.

Against this list of technical advantages you claim that barrel charging ports are "nonstandard" and "obsolete" — not because of any actual USB-C functionality, nor even because there are more USB-C-chargeable devices in the world than devices with barrel connectors, but just because USB-C is newer and currently fashionable. The maximally charitable interpretation of your post is that USB-C chargers are capable of providing a range of different voltages, so the complexity of voltage conversion goes into the charger instead of your headphones. But that's an extremely weak argument; a buck converter capable of deriving 5 V 300 mA from, say, 19 V is already much smaller, lighter, and cheaper than a pair of wireless headphones, and adding USB-C charging support to your product also requires a significant BOM cost, and the necessity to operate on 5 V as well as whatever it prefers, though maybe less weight than the buck.

What's inappropriate is that you're attempting to dictate decisions of technical functionality on the grounds of mere fashion and social approval, then shaming others for disagreeing with your judgment rather than supporting it by any actual arguments.

I predict that >99% of devices made this year that can only charge through USB-C ports will be nonfunctional in 15 years. That is, they are cheap trash, designed to be discarded rather than repaired. You should be ashamed of yourself for attacking my social standing to convince people to accept this inferior technology. The form of your argument — a veiled personal attack — makes it unworthy of being posted on this site, or, actually, anywhere.