Disclaimer: I am a moderator on Computer Science Stack Exchange. While I try to judge this proposal on its own merit, it is likely that the time and energy I have invested in CS.SE influences me.
I'm afraid that broadening the scope in this way would destroy the existing community. A Stack Exchange site is defined by two things: the kind of questions it accepts, and the audience it attracts. Even though each question is in principle judged on its intrinsic merits, the long-term effect is to create a community.
On this site, the community is centered around researchers in theoretical computer science. Participants tend to be researchers in TCS, researchers in other fields, or graduate students aspiring to become researchers. The participants who are welcomed are generally those who came with the expectation of participating in a community dominated by TCS researchers.
I do not see a problem with allowing more applied questions. As long as academics and people who want to fit in with academics dominate the site, that isn't a problem. It may be difficult to bootstrap an applied CS community (it would have been a lot easier to do when the site was young), but if it works, it won't change the tone of the site, and if it fails, the site won't have changed.
On the other hand, opening the door to more basic questions means opening the door to a broader audience. This should be a carefully controlled process. In particular, I advise you not to try to draw on Stack Overflow as an audience base. A majority of Stack Overflow does not know or care what it means to be a scientist. The kind of people you would attract are those who now post on Programmers. If you attract those people, be prepared to moderate their content. And to moderate them.
Reacting to specific points in your proposal:
We now have a natural forum (cs.stackexchange.com) for the more "basic" algorithms questions, and the cstheory "brand" is well established as a 'research-only' venue. So we have an easy process to shunt questions that are obviously undergrad level.
Keep in mind that CS.SE is not exclusively for basic questions. It is for questions at all level, ranging all the way from CS 101 homework to applied research (and even research in theory, but we suggest CSTheory.SE to the rare asker who comes with a theory question that seems to go unanswered because it is too hard).
excluding questions from people who might be 'research-level' in a sub area but aren't experts in some other domain
From what I see (I admit to not following CSTheory.SE very closely), this already happens: as long as there's a feeling that peers are talking with peers, questions tend to be appreciated, left open and answered.
creating the impression of an unfriendly site (which is a bigger problem in terms of maintaining the audience)
I think the community is doing an adequate job of retaining the audience it likes in and keeping the undesirables in.
All in all, while the current guidelines may be stricter than this, I think an intelligent application of the existing policies already gives you what you want.