advantages of jacks + wires: reliable, 140 year old industry standard, plug-and-play, universal, cheap, easy to repair, doesn't require battery, doesn't require configuration, doesn't get out of sync, cannot be hacked by a third party.
downsides: sometimes all those wires tend to mix and make knots.
downsides: can't move really far when plugged into stationary device, breaks a lot (at least for me it's almost always the plug or cable that breaks), cable picks up random noise
upsides: my very old thingamajig with a broken display doesn't support anything else
If they break a lot, you should find better headphones.
My JLab Audio Diego earbuds have lasted for the past two years, and I don't treat them well—they stay in my back pocket, and have experienced several trips through the washing machine.
And if they ever do break, the cost of a replacement is $15. That's barely more than the cost of the headphone jack to lightning adapter that I would need if I upgraded from my 6S.
And they have a flat cord that very rarely gets tangled.
advantages of jacks + wires: reliable, 140 year old industry standard, plug-and-play, universal, cheap, easy to repair, doesn't require battery, doesn't require configuration, doesn't get out of sync, cannot be hacked by a third party.
downsides: sometimes all those wires tend to mix and make knots.