why bother with Being?

Heidegger is quite aware that asking about Being raises the question of relevance. What motivates him to write about it? First, he points out, there is the fact that this is a theme addressed by Aristotle, and a certain respect for giants in the field inclines us to take it seriously when, not just anyone, but a giant raises a topic. Also, the available answers to the question of what Being is seem unhelpful – it's undefinable, it's the most general thing around. Heidegger puts it this way:

Up to now the necessity of a retrieve of the question [of Being] was motivated partly by its venerable origin but above all by the lack of a definite answer, even by the lack of any adequate formulation. But one can demand to know what purpose this question should serve. Does it remain solely, or is it at all, only a matter of free-floating speculation about the most general generalities – or is it the most basic and at the same time most concrete question?
Bisher wurde die Notwendigkeit einer Widerholung der Frage einmal aus der Ehrwürdigkeit ihrer Herkunft motiviert, vor allem aber aus dem Fehlen einer bestimmten Antwort, sogar aus dem Mangel einer genügenden Fragestellung überhaupt. Man kann aber zu wissen verlangen, wozu diese Frage dienen soll. Bleibt sie lediglich oder ist sie überhapt nur das Geschäft einer freischwebenden Spekulation über allgemeinste Allgemeinheiten – oder ist sie die prinzipiellste und konkreteste Frage zugleich? (§ 3)

And of course the italicized part is Heidegger's own view. Additional support for the importance of the question of Being can be found in the fact that, according to Heidegger, there is an "average and vague understanding of being / durchschnittliche und vage Seinsverständnis" (§ 2). The "question of Being" is one that we all share; in writing this text, Heidegger is addressing a theme that is present everywhere in our own lives, and in this sense the inquiry is not 'meta' 'physical' (not 'above' 'life'). As he says: "No matter how much this understanding of being wavers and fades and borders on mere verbal knowledge, the indefiniteness of the understanding of being that is always already available is itself a positive phenomenon which needs an elucidation. / Dieses Seinsverständnis mag noch so sehr schwanken und verschwimmen und sich hart on der Grenze einer bloßen Wortkenntnis bewegen – diese Unbestimmtheit des je schon verfügbaren Seinsverständnisses ist selbst ein positives Phänomen, das der Aufklärung bedarf." (§ 2)

Much of § 3 is taken up explaining the relation of Heidegger's book to the sciences and other philosophic attempts to discuss being. Just a couple of moments that seem important to me:

A science's level of development is determined by the extent to which it is capable of a crisis in its basic concepts. In these immanent crises of the sciences the relation of positive questioning to the matter in question becomes unstable. Today tendencies to place research on new foundations have cropped up on all sides in the various disciplines.
Das Niveau einer Wissenschaft bestimmt sich daraus, wie weit sie einer Krisis ihrer Grundbegriffe fähig ist. In solchen immanenten Krisen der Wissenschaften kommt das Verhältnis des positiv untersuchenden Fragens zu den befragten Sachen selbst ins Wanken. Allenthalben sind heute in den verschiedenen Disziplinen Tendenzen wachgeworden, die Forschung auf neue Fundamente umzulegen.

The above reminds us a bit of Thomas Kuhn's book on Scientific Revolutions, no? Could we say: when science is not in crisis, its 'being' is hidden. When there is a crisis, when we are in transition from one paradigm to another, previously hidden being is to an extent available for viewing? Heidegger continues:

The discipline which is seemingly the strictest and most securely structured, mathematics, has experienced a "crisis in its foundations."....Relativity theory in physics grew out of the tendency to expose nature's own coherence as it is "in itself." As a theory of the conditions of access to nature itself it attempts to preserve the immutability of the laws of motion by defining all relativities; it is thus confronted by the question of the structure of its pre-given area of knowledge, that is, by the problem of matter.
Die scheinbar strengste und am festesten gefügte Wissenschaft, die Mathematik, ist in eine "Grundlagenkrisis" geraten....Die Relativitätstheorie der Physik erwächst der Tendenz, den eigenen Zusammenhang der Natur selbst, so wie er "an sich" besteht, herauszustellen. Als Theorie der Zugangsbedingungen zur Natur selbst sucht sie durch Bestimmung aller Relativitäten die Unveränderlichkeit der Bewegungsgesetze zu wahren und bringt sich damit vor die Frage nach der Struktur des ihr vorgegebenen Sachgebietes, vor das Problem der Materie.

The implication of the above is that "matter" itself has become problematic as a foundation for science. Or am I misreading Heidegger here? Am I right in thinking that Heidegger is mentioning these developments in science to buttress the case that the problem of being is important and should not be dismissed as airy speculation? If he's right that there is an average understanding of being that just isn't worked out, can we, Heidegger's readers, make the issue of being more explicit ourselves, even before we go further in Heidegger's discussion of it? Can we think of 'examples' of being?

Perhaps there is a hint in Heidegger's discussion of sciences that enter into crisis, such that "the relation of positive questioning to the matter in question becomes unstable / das Verhältnis positiv untersuchenden Fragens zu den befragten Sachen selbst ins Wanken."

It's in the transition from one kind of being to another that we can glimpse 'being'. Take a fictional example: Tony is a highly regarded professor who gets his way a lot where he works. But every weekend he goes to his parents for dinner, and there the conditions are recreated in which what he does professionally isn't taken very seriously, his will is disregarded, and he finds himself engulfed in an environment he cannot escape, obeying rules and playing roles that would surprise his co-workers.

Is that the kind of thing Heidegger is talking about when he suggests being is "the most basic and at the same time most concrete question / die prinzipiellste und konkreteste Frage zugleich"? Or is that a trivialization of it?