Learn English – “have had to do something” vs “must have done something”

You have clearly misunderstood the usage of modals and their time reference. Incidentally, I shall explain it to you with some examples before I jot some points down on the paper.

To start with, modality is a branch of linguistics which enables and allows us to express, or emphasize the (in)ability, (in)capability, (im)probability, obligation, (im)possibility, permission, necessity, (un)likelihood, (un)certainty, and so forth of an action or event.

Modal auxiliaries, often referred and known as 'modals' or 'semi-modals', in the English Language are:

shall, will, would, can, could, must, have [got] to, gotta( informal contraction ), need, had need( archaic ), had better, should, ought to, oughta( informal contraction ) and so on.

e.g.

will - expresses assumption, disapproval, politeness, habits, or even certainty of the present

had better - expresses strong advice or order

need - [usually negative] expresses immediate necessity or, sometimes, things that are not necessarily true

........

A majority of these modals have their perfect variants that link the previous event with this/that point of time. Furthermore, perfect modal auxiliaries are formed by the following method/pattern:

a modal's root word + have + the past participle verb

But they don't necessarily refer back to the past; in addition to that, they can describe the completion of a future event, that is expected/considered to be completed before some action, as in:

By the time I get home, the sun will [already] have risen.

As I was saying,

I should have done it. ( " = but I didn't even though I was supposed to do it - expresses one's regret of the action - ");

I would have done it. (" = If I [had] had a chance, I would have.");

I must have done it. (" = I certainly did it - No doubt - ");

I could have done it. (" I didn't although I could - could express one's missed opportunity ");

I can't have done it. ( " -certainly expresses impossibility of the event -synonymous with mustn't have + past participle , but the former is used more frequently since the latter may sound verbose to some" );

To return to the previous point, although most of the modals are not backshifted in reported speech such as : should, would, had better, needn't, and others; they mean the same in the reported sentence as their meaning was the same in the non-backshifted sentence.

He claimed that she must have gone out of the house. ( " emphasizing the statement that she had definitely gone out the house at some moment of time ");

He proposed that she [should] clean her apartment. ( " the obligation still took place at that time - no backshift, while "will" will have its counterpart, that is, "would" as long as the reporting clause keeps its past form and has to collocate with the modal - ");

CONCLUSION:

To wrap this up, your sentences do differ in terms of their aspectual meaning.

Over the past 5 years or so, he's had to look after his mother. (" refers to his obligation of looking after his mom, over the past 5 years which is undoubtedly the present perfect. ");

WHEREAS

I was sure she must have been swept off her feet. ( " here the perfect modal " must have been " links the previous event with that moment [of time], which precisely describes that she was definitely swept off her feet ");

Quick have-to semi-modal tense reference:

present - present perfect - past - past perfect

have to/must - have had to - had to - had had to -

I hope I provided you with elaborate information on this subject.