Torzon Decisions Every choice this involves, with what each option costs you
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Phone or computer

The honest objection to mobile is not technical. It is that mobile makes the one habit that matters annoying enough to skip.

A computer you control

What you gain
Signature checking is straightforward, so the habit survives. You can see what you are copying and control what else runs.
What you give up
Not always available, and not always private.
Suits
Anyone who can. This is the default.

A phone

What you gain
Available, private in the sense that it is yours, and generally the device people actually have.
What you give up
Checking a signature is inconvenient enough that people stop, and stopping is worth more than every other difference combined.
Suits
People who will genuinely still check, and who have worked out how before they need to.

A shared or work machine

What you gain
Nothing.
What you give up
Everything on this site assumes a machine you control. Verification runs locally, so a machine that can be made to lie makes the whole exercise theatre.
Suits
Nobody. This is one of the few hard blockers here.

Why the usual objection is the wrong one

People argue about whether a phone is inherently less secure, which is a long argument with no clean answer. The practical objection is narrower and much easier to settle: on a phone, copying a signed block into something that can check it is fiddly, and fiddly things stop happening.

A tool that makes the load bearing habit annoying removes the habit, and that is a larger risk than any property of the platform itself.

If you use a phone anywayIf you are going to use a phone, work out how you will check a signature on it before you need to, not during the first login. Doing it once in advance is the difference between a workable setup and one that quietly degrades.

The other differences

ComputerPhone
Checking a signatureStraightforwardFiddly, which is the whole problem
Seeing a full addressEasyTruncated by default, which hides the part that matters
Knowing what else is runningReasonablyMuch less so
Backups and syncUnder your controlFrequently on by default and easy to forget
AvailabilitySometimesAlways, which is why people use it

What tips it

Whether the address is truncated on your screen. That single detail decides more than anything else here, because a forged address matches the opening characters and differs in the middle, and a display that shows you the start and an ellipsis is showing you exactly the part that always matches.