Relationship between "received" signal power and "transmitted" energy per bit?
You are correct that it could be argued that every physical channel will introduce attenuation. In digital communications, however, it is common to define "channel models" that simplify the equations and make the problem easier to understand and to solve.

The most popular model is the "additve white Gaussian noise" (AWGN) model, where the only effect of the channel is to introduce noise. In other words, there is no attenuation. In that model, Sklar's relationship between power and bit energy is correct. This model is very popular because, in many cases, you can ignore the attenuation by assuming an appropriate gain mechanism in the receiver.

Of course, in many other cases the AWGN model is not appropriate. In the wireless channel, for instance, the channel gain is so fundamental that it gets incorporated into the model. If the channel is narrow-band, then the relationship between power and bit energy is similar to what you propose, with $\alpha$ random and possible time-varying.