I've bought a new analogue mackie mixer that I'm very happy with, but if I need one effect it would be compression. The mixer comes with 16 builtin effects and not a compressor. Is it expensive to make or why is compression not included? Instead I have reverbs and echoes which are not very applicable for the dry sounds of a small room that I want to create.
While you often see compression in the effects section of editing software, it is dynamics rather than actual effects. In the traditional sense in the live world, compression is not considered an effect. The software world simply does it that way because they are all software filters, but even then they are often in a dynamics category.
Compression, Expansion, Gating and Limiting are all dynamics. I'm not sure if the effects hardware could do compression, but the controls for the parameters on the effects are certainly too limited. You need attack, release, ratio, threshold at least and gain and soft/hard and auto attack/release options are common. You can't adjust these with the very basic effects controls provided in the board.
There are boards that have built in compression, but they list it under dynamics normally. There are also stand alone compression units you can get that you can use the inserts to feed the signal to.
Well, first off – all professional digital mixers today now have per-channel compressors, and more and more analogue ones also begin to have them, at least on some channels. Usually, there will be just one knob, basically controlling the threshold but possibly also a combination of ratio and gain. That's not as versatile as a fully-featured rack compressor, but still often quite useful.
As for why compression is not included in the multieffects section: those are send effects, i.e. effects that run in parallel to the main mix bus on a send bus. By routing a bit of one channel to the FX bus, you get some e.g. reverb, in addition to the dry sound you get on the mix itself. These effects are usually linear, which means you can route multiple channels to the same FX instance and the signals won't interfere, and reducing the input level is fully sufficient to control the "strength" of the effect.
But this doesn't work for insert effects such as EQ, compression, distortion etc.. Those need to get the entire signal of one single channel, and for full control there shouldn't leak any unprocessed signal component directly to the mix. And you can't properly control the strength of the effect by modifying the input level (in the case of a compressor it would kind of work, but not nicely). So such effects either need to be fixed in one channel strip – that's what done with the channel EQs. Or you need some way to patch both the effect input and output to an arbitrary channel. The easiest way to do that is to use a rackmount compressor, put a Y-cable in its I/O jacks, and plug the stereo jack in the channel's insert connector. This way the whole signal will be routed through the FX processor, and only afterwards it's allowed to pass into the mix at all.