Could we no just as well define the efficiency of an engine as ϵ = |W| Q_out | rather than as ϵ = |W|/|Q_in|? why don’t we?

The thermal efficiency (ε) of an engine is defined as the work the engine does per cycle (“what you get”) divided by the heat energy it absorbs per cycle (“what you pay for”), or
ε = Energy you get / Energy you pay for
= W/ Qin.
= Q_in-Q_out/ Q_in
Here Q_in is the input heat energy of source and Q_out is the output heat energy of sink.
Therefore efficiency ε of an engine is defined as the ratio between useful heat (heat converted into work) to the total heat supplied to the engine.
The efficiency of an engine measures the amount of energy (W = Q_in-Q_out) that we can extract from the original energy or input energy (Q_in) of that engine. That is why we could not just as well define the efficiency of an engine as ε = W/ Q_out rather than ε = W/ Q_in.