When reformulated to speak of legacy and (im)mortality, I think this is fertile grounds for a really interesting thesis.
Can we say that LEGACY is a theme, related to fertility, but which contextualizes the importance of progeny and childlessness?
I can kind of see where you are coming from. For example, Lady Macbeth's inability to have a child or keep one alive is something that greatly frustrates Macbeth, as no matter how secure he makes himself, the lack of an heir means that the prophecy of the witches is something that is going to come true whatever he does or doesn't do. However, I must admit to being skeptical about infertility being the real issue in Shakespeare's tragedies.
I too would agree that the tragedies aren't really about fertility or regeneration. The want of personal power is at the heart of each, but none of the main characters even talk about the future of their kingdoms or even their legacy; even less-so children or a future that is directly tied to their heirs or lack thereof.
I also have to agree that I do not see fertility in the plays, especially Macbeth. Macbeth has no children and does not think that he will. He actually is angered by the fact that Banquo's children will be kings.
In that death and dying are thematically important in Shakespeare (it is even evident in his sonnets as he calls upon his words to vouchsafe immortality), one might infer that the reverse is implied. However I think you'd have a hard task at hand to prove this inference was an overt objective in Shakespeare's plays rather than a binary reading through the lens of deconstruction theory.
I don't think fertility is the most overarching theme in Shakespeare. You might broaden it to family, and you'd have a case. Romeo and Juliet, Hamlet, Macbeth and the others all have family elements, of which fertility can be a subset.
In terms of ageing and infertility, I can see this in Macbeth. For example, though Lady Macbeth states that she has nursed a child, but no children are mentioned in the play.
I have given suck, and know(60)
How tender ’tis to love the babe that milks me (I.vii.60-61)
We can assume she has had a child but no longer does. If she had one child and no more, this might literally indicate infertility. That Macbeth is enraged that Banquo's "issue" will become kings. He has lost his eternal soul (in killing Duncan) and will not be able to pass what he has murdered to get, to his children.
The ageing motif applies to how worn and beaten down Macbeth and Lady Macbeth are after they have murdered the King, and Macbeth has assassinated Banquo and Macduff's family. The vibrancy of this couple has fallen off, and they shuffle along, tired and unsatisfied.
There is also a sense of infertility (and regeneration) figuratively, as Macbeth's efforts to become powerful and take the throne do not yield any "fruit." He is hated and feared, not loved and respected as Duncan once was. His kingdom will not endure after his death, and no one will offer up praise or prayer at his death.
It is interesting when you note the trees that are hewn down to cover Malcolm's soldiers as they move on Macbeth and his castle. The landscape of the play has been very grey—as has the mood since the witches opened things "in the fog and filthy air" at the beginning. It is only with Malcolm that change arrives, and it is announced with a vibrant green, which may symbolize fertility and regeneration as a new king will soon be crowned and Scotland will have new life.
I cannot say that I agree, unless it's with a highly qualified agreement. If we relate fertility (directly) to potency, then I can agree that Shakespeare's tragedies concern a desire to attain power. I'd need to be convinced, however, than fertility, potency and regeneration are (all three) connected and equivalent.
I'd point to Hamlet as a tricky case for your argument and ask:
How is Hamlet about fertility or regeneration?
I'm not sure I see much overt fertility and regeneration in the plays, except possibly by implication in the very final scenes. At the end of Hamlet, corpses are all over the stage; at the end of Macbeth, Macbeth's head has been severed from his body; at the end of Lear, Cordelia is dead, and so is Lear; at the end of Othello, Iago is defiant and unapologetic; etc. How are you thinking of fertility and regeneration? I may be misunderstanding what you mean.
Sorry, I forgot to mention "the new-planted orchards" for all Romans in Caesar's will, III.2. 238. This reference may serve to establish a clear link between leagcy and fertility in the play.
In Julius Caesar, interestingly, the testament read by Antony is first addressed to "the Roman citizen": "he hath left them you and to your heirs", III.2.249-250. In addition, Caesar's heir is Octavius, his nephew, who is to become "another such Caesar" at the head of the Roman Empire and not of the Roman Republic: "Here was a Caesar! When comes such another?", III.2.242. The conspicuous use of antonomasis ("a Caesar") is telling.
Therefore, "legacy" (even in the literal sense, if not in the figurative sense) and "fertility" are closely linked in the particular context of Julius Caesar.
I think # 5 is convincing and I couldn't agree more. A.C. Beardsley in Shakespearian's Tragedy assumes that Macbeth deals with childlessness. The beginning of Julius Caesar also deals with this particular topic : "Forget not in your speed, Antonio, // To touch Calpurnia, for our elders say // The barren, touched in this holy chase, // Shake off their sterile curse," I.2.5-8. Portia and Brutus are a childless couple. Assuredly, King Lear and even Romeo and Juliet can also be interpreted in a similar fashion. Of course, the central theme of the best-known of his tragedies remains the downfall of kings whose lust for power leads to moral deterioration.
To be continued, I hope...
I meant aging and infertility and the striving toward fertility and regeneration. For example, "the yellow leaf" (5.3.24) at the end of Macbeth is opposed to the green forest trees that have ceased to conceal (or screen) the marching soldiers.