Is there a reason why we don’t supply power to a 2.5 mm or 3.5 mm jack?

It's possible, and I've seen it done (the gear in question being a wideband amplifier for an EMC probe set), but for isolated low voltage only. The main drawback is the possibility of shorting the plug supplying power as swipes past the outer (ring) conductor. While it might be acceptable for a specialty power input with limited voltage and current, it obviously would be a dealbreaker for line voltage.

For low-voltage it's better to adopt either the barrel type connector, or even better, USB if your device uses 5V. These are commonly available as off-the-shelf types for AC/DC adapters. They're well-known and they don't short out as you plug them in.

But you asked about line voltage too. Let's talk about that and why using a phone 'tip-and-ring' style connector is a spectacularly bad idea.

• Insulation distance. Line voltage needs more stand-off (insulation) distance than is possible with a mini (3.5) or micro (2.5) phone jack.
• Exposed terminals. Line voltage present on the delivery-end plug poses a shock hazard.
• Tip-to-ring short during insertion. As mentioned above, phone jacks have a number of ways they can short out as they're being plugged in.
• Current capacity. Phone jacks aren't designed to carry a lot of current. They would fry in short order with any kind of realistic load.
• Confusion with existing uses. It would be all too easy to plug an audio cable into a phone jack being used (mistakenly) as line voltage.
• Plenty of options for line-in. The market is rich with many good, compact connections for line power.

ADDENDUM: We're not talking about 'phantom power' applications. This is perfectly fine on phone jacks - it's extremely common in fact for microphones and musical instrument pickups. This power is limited in voltage and current so poses no harm as long as it's isolated from the line.

What happens when the tip slides across the other contacts? TRS connectors are not ideal for power delivery because incorrect shorts can happen as the connector is mated.

It has been used for power in the past, but not so much any more, because it has proven to be a bad idea to use one connector for multiple purposes. Imagine the damage when accidentally plugging 12V supply into audio output or microphone input.

That is also the reason why you don't want to use USB connectors for anything else than USB or HDMI connectors for anything else than HDMI. It has been already confusing enough to use 3-pin XLR for line level audio, mic level audio, digital AES/EBU audio, and DMX512 lighting control, and damage is possible when connecting wrong interfaces together, or requiring suitable cabling for proper data transmission even if the connectors are identical.