A recording console has two types of signal source. One is from the microphone and line inputs. The other is from the already-recorded signals on the multitrack tape. To record overdubs, these must be mixed together for the monitor mix and headphone foldback.
The simplest way to arrange this is to have a console with many inputs - at least the number of tracks on the multitrack (often up to 48), plus the number of microphones you need to use simultaneously. A total of 72 channels would suit most applications.
In this example of a 72-channel console, 24 channels can be dedicated to inputs, the other 48 channels can be used for monitoring the already-recorded signals on the multitrack recorder.
This 'all input' architecture is easy to understand and operate, but it requires a lot of channels.
There have been a number of consoles designed specifically in this format, notable by Amek and Soundcraft. However, any console with sufficient channels can be used this way.
Since all-input is so easy to understand and use, many engineers work this way, even on an inline console.