DIY/OSHW Pick/place seems like a good idea on the surface, but the more you think about it the less sense it makes.
I have done a LOT of thinking about it - originally looking at starting with an X/Y plotter, and ending up buying an old commercial P&P machine when I realised that DIYing was a lost cause.
The problem is that it is only worth doing if you end up with something that is actually useful. This is where the idea starts to fall apart before you even start looking at the technical issues.
Let's start by looking at production volumes:
If you're only placing a few tens to hundreds of parts, it is always going to be quicker to do it by hand than set up even the best, most user-friendly P&P machine in the world. You also have to consider that pretty much any feeder design will waste a few parts on leading and/or trailing end of the tape, that you need to have parts on tape/tray etc. in the first place. for small builds the wastage could be more then the parts used.
If you're doing tens of thousands of parts upwards, professional subcontractors will always do a better job because it's what they do all day, every day and they are better at it than you will ever be.
So that limits your potential usefulness to a low-to-mid range of volume between hand assembly and subcontract. Or if you need fast turnaround or extreme flexibility.
Next, machine capability.
You don't want to have to constrain your design too much in terms of part types, so any useful machine needs to at an absolute bare minimum place 0603s and SO parts with a high yield. And if you're spending money building a machine, you will be limiting usefulness if you can't also deal with 0.5mm QFPs and maybe 0402's as well.
You also need to be able to work on big enough panels to not have to keep reloading, and not limit the type of boards too much. Something like 200x300mm is probably a reasonable minimum, which also corresponds roughly to the typical max size of cheap toaster ovens and low-end stencil printers.
On the basis of needing a placement accuracy an order of magnitude better than the smallest feature size, this means moving a placement head to an accuracy of 0.05mm over the whole 200x300mm placement area, including repeatability, temperature dependence, wear, backlash etc.
This inevitably means expensive mechanics and very solid construction.
I don't think there is much scope to be clever with on-the-fly vision to correct mechanical errors, as the pads are covered in solder paste.
Speed isn't necessarily a major issue, as long as it is at least a similar order to hand placing, and needs minimal hand-holding so you can leave it to get on with it. The upper bound is how long the solder paste takes to dry out.
However if you're already spending enough to get the mechanical precision, it's going to be worth spending a little more to get reasonable speed.
Then there is the feeder problem. This is the killer.
You will have parts on tape (8,12 and 16mm, plastic and paper), tubes and trays.
Yes you can passively feed tapes (static strips) but this is a pain for parts that are used in any quantity. It also uses up placement area.
Mechanical tape feeders are hard to do well - what initially seems like a simple problem is deceptively complicated - pulling off the cover tape, not losing too much in leaders/trailers, and making the mechanism narrow enough to get a sensible number of lanes.
And you need quite a few of them, in different sizes. You could make an adjustable one for different tape widths but then you can't stack as many side-to-side.
So in summary, yes you can build a cheap, simple P&P but it will be a useless toy and therefore a waste of time.
A useable one would take a lot of work, not be cheap due to th emechanical precision and quantity of mechanics for feeders, and then still only address a subset of the possible assembly jobs in terms of volume, size etc.
There are many, many more useful OSHW projects to be designed before it is worth doing a P&P.