The reason current is most often measured by multimeters in a series connection is that current is usually measured via a
current shunt. Where the voltage drop across a
shunt resistor is used to find the current via Ohm's law. So the current must flow through your resistor where you want to measure the voltage drop relative to the current passing through it. A
Shunt resistor is usually a small resistance like .001Ω, so the voltage drop is very small (5 mV @ 5A) and is for most applications of little impact on the circuit you are measuring.
There may be a meter on the market that measures current magnetically using a coil or with hall effect sensors, or some other method internally, but these would still require the path of the electrons to be routed uncoupled through the sensor.
If you think of voltage like water pressure where water does not need to be flowing for it to be present and measured then you can see that knowing the overall water pressure tells you nothing about how much water is moving. If you stand in a stream you instantly know if water is flowing or not. All a meter does is stand in the middle of the stream and figure out how much water is flowing relative to how much pressure the water is exerting on it.