Intuitively, I would be inclined to think either the keyboard matters more to your target market than cost or it doesn't, and in the latter case you might as well use a membrane keyboard, being the cheapest option, but empirically, chiclet keyboards were more common.
Target market is cost. When targeting for example text entry as a business case, the keyboard has to comply with the expectation and use case. Here one may use cheaper switches (and risk longtime maintenance cost) but can not in any way go for chiclet or membrane. Thus soemething like 100 USD or more on the keyboard alone is a must. And a reason why reliable long term business keyboards always have been of higher cost.
Now if the target is to build a computer way below a 5000+ mark, removing parts is the first step, and what remains needs to be stripped down.
In case of machines like the PET, Apple 2, Atari 400 or similar, the goal was to make a (mostly complete) basic computer available at all. Any keyboard, as funny as it is, is better than no keyboard. Cutting down on keyboard cost is a way to go. Especially considering that a full ASCII keyboard with standard keystroke was in 1977 still more then 100 USD retail (*1). These machines have been constructed prior to 1977, so selecting an affordable keyboard design is of great influence to the machines final price tag. Even including the hope to go for large quantities and get a hefty discount when ordering the parts.
I'm curious about the thought process that went into this; was it the case that a chiclet keyboard is still pretty cheap, or that a membrane keyboard was just considered too abominably bad to be tolerable?
For Commodore the choice was rather clear. It's the same keyboard design they already used for their desktop calculators. They already had a working relation with Mitsumi, and the PET keyboard was just a new variant to them (*2). No need to explore a different technology and pay (comparatively) large setup cost for a new machine where they weren't sure if they can sell more than a few hundred anyway. They did just run along with other keyboards made.
So for Commodore it was the cheapest way to start into microcomputers - much the same way as IBM did go with a keyboard based on others they were already manufacturing.
Or why the Apple 1 was sold without a keyboard - adding another 100 USD would have for sure killed the 666 USD sales price :))
We do have an estimate for the cost of a mechanical keyboard: https://en.wikipedia.org/wiki/Commodore_64#Manufacturing_cost puts it at $10.
Not really, as that was the production cost after about 4-5 million pieces. Orders for new keyboards by Commodore were not made for a few hundred as in the beginning of the PET, but for next to 100,000 per month. The interesting issue here is that the C64 keyboards were still at 10 USD at that time.
Cost at start must have been considerable higher. Even including the fact that it's 'just' a modified VIC-20 keyboard and the first batch was already set to 5,000 units.
If the cost to the manufacturer of a chiclet keyboard was, say, $2, that would indicate one rationale for its use, and if the cost was $8, that would indicate another rationale.
Mind to explain what rationale you're implying?
Is there any known data for the cost of a chiclet keyboard, or estimate of how it compared to the other options?
No, but considering that Commodore already had Mitsumi supplying their calculator keyboards, it must have been acceptably low - I'd say at that time (1976) already below 20 USD, making it a real bargain.
*1 - Even two years later, in 1979, 70+ USD was acceptable price when browsing thru late 1979 issues of Kilobaud and Byte. So the prices for keyboards were not only high but also only declining slowly.
*2 - A look at the Advanced Scientific Calculator Model 1540 tells much of the story. The 1540 was designed at the same time (1976) as the PET and features the same chicklet keys - much like other Commodore desktop calculators of the same time. Essentially it's an SR-1500 with larger keys and display for dektop use.