Why are continuously emitting radio pulsars not detected?

[Baluncore]

It might still be possible in the time domain, however. I think what you'd look for is a nearly continuous but still periodically varying source, as if the beam was nearly, but not exactly, aligned with the rotation axis.

A pulsar is a noise source that pulses in a noisier background. The detected signal from the brightest pulsar, fed in real time to an amplifier and speaker, can just be heard in the background noise.

Given sufficient time, you can gather data with about a 2 kHz BW, then FFT, and Power Spectrum Accumulate, deep into the noise, to see what is hidden in there. If you find a blip in the PS, you can run it again on the same patch of sky, to see if it is still there, and repeatable. Once you have an idea of the pulse rate, you can take longer time samples, to get better estimates of the rate. You can then accumulate power in a circular time buffer, to see the shape of the pulse. But what if the pulse is an almost flat sinusoid?

Either you have reliably detected a pulsar, and measured its period, or you have not. I see no way to tell the difference between a dim pulsar in noise, a pulsar being seen side-on in noise, or one almost end-on in noise.

The search for the pulsar with the flattest sinusoidal pulse, will take forever, and cannot resolve any question.

Observatory time is expensive. There is little point in investing the huge amount of observation time, needed to dig the smallest signals out of noise, if those signals are so small, that they cannot be categorised meaningfully.