The expression "a kick in the ass" (or, more mildly, "a kick in the pants") is sometimes used to refer to jumpstarting an individual, or getting a situation back on the right track, as in:
"Our son needs to get a job!"
"Yes, he needs a good kick in the pants."
It stands to reason, then, that "boot" can be substituted for "kick," since that's the net result, when the one doing the kicking happens to be wearing boots.
He himself felt sorry for the people who were in horrible pain, but some need the good boot in the ass. (J.E. Jackson, Camp Pain: Talking With Chronic Pain Patients, 1999).
If you want, check out this Ngram. You can see that all these phrases are used, but kick in the pants seems to be most common.
Your example usage:
Does Google need a strong engineer to put a boot in the ass to develop the next XXX ...
reads a little awkward, since it's usually an outsider, or one with some authority, doing the kicking, and it's hard to tell whose butt is going to be kicked in that sentence. (Google's?) If the "strong engineer" is in charge of a group of engineers who are developing XXX, then the expression might work, but I'd probably write more like this:
Google needs a strong engineer to put a boot in the ass of the team developing the next XXX ...
The phrase is definitely correct idiomatic usage.
To make a case for something, when something is a noun (or pronoun), is to provide good reasons why the named thing should be considered for use at whatever tasks that thing is normally used for.
You could consider it to be a shortened form of make a case for you to purchase something.
If the device in question "doesn't make much of a case for itself", then it is failing to provide any compelling reasons for you to purchase and use it instead of one of the available alternatives; we can presume that its competitors are more capable, or cheaper, or easier to use, or better-looking, or some combination of those.
Edit to add:
In particular, the "for itself" is appropriate because a salesperson could "make a case for the phone" by explaining its benefits and features to you. In the absence of a salesperson, the phone has to have enough features and benefits that you can discover without assistance: the phone has to sell itself, or "make a case for itself".
Best Answer
Up is not always the antonym of down, particularly in verb phrases such as put up, shut up, show up, or end up. In this case, "put up your books" is essentially the same as "put away your books."
The translation doesn't make sense only if you mistakenly translate the words put and up as two separate words, instead of as the transitive verb put up.
Besides meaning to put away, put up can also mean to erect (as in, the city put up a new building), to hang, as a picture (put up some posters for next week's concert), to tolerate (she put up with his bad manners), to provide housing for (we put up our in-laws for a week), or to place for sale (the estate was put up for auction last week).