As you say, most things run on DC, and rectifying AC to DC doesn't care about line/neutral reversal.
It does create some safety issues in certain applications as I described above.
It can cause some things to misbehave. For example, in home energy monitoring, where you clip one or more current transformers around a circuit's line conductor(s) to measure the current consumption of that circuit and connect an AC-AC transformer (to reduce it to a lower voltage, to make it suitable for export on an extra-low-voltage finger-accessible connector like a barrel plug, and so that it can be measured by an analog-to-digital converter) to the unit, so that the unit can measure voltage (and thus work out power) [2], then if line/neutral is reversed, its observation of what it thinks is line will be at the wrong point (relative to its observation of neutral) when computing the power being transferred. This will result in the device telling you that the circuit is exporting power (when it is actually importing), or vice versa.
It all depends upon the application. In most instances, line/neutral reversal is fine; and indeed with non-polarised plugs, unavoidable. However it should be avoided if possible.