Modal verbs (eg must, can, may, might, would, will) are among the categories of language items that evolve very quickly, and are gradually disappearing from the language. That was one of the topics discussed on Radio 4's Word of Mouth programme a couple of weeks ago, but which will be on iPlayer (here) for a while yet.
Evolutionary biologist Mark Pagel said that about 50% of the vocabulary of a language changes over a period of 1500 to 2000 years. Some categories of words eg numbers, especially the numbers 1-5, and pronouns, evolve very slowly - the words we use today are related to those used 2000 years ago - but other categories of words - nouns, verbs, adverbs, conjunctions and prepositions - evolve rapidly.
Linguist Bas Aarts has examined several corpora and could tell from that exercise that modal verbs are gradually disappearing. For instance, shall was once used to denote intention (as in Churchill's famous speech beginning 'We shall fight on the beaches'), whereas will denoted volition. Will or 'll, however, is now taking over from shall, which is hardly ever used by younger speakers.
There has been a 50% decline in must over a few decades. The linguists on the radio programme suggested that it has too much of an authoritarian feel for modern sensibilities and that the language is being democratised. Negated modals eg oughtn't and shan't are rarely heard these days (and some that were once common, eg mayn't and the spelling of shan't as sha'n't, have completely disappeared).
May is an interesting one. It is still used when referring to possibility (eg he may be in his office), but when used in the context of permission (may I leave the room, please?), it is being edged out by can. That has happened over a few decades; when I was at primary school we were pulled up for saying 'Can I...?'. Linguist Laura Wright suggested on the programme that one of the reasons was that the vowel sound in can in a sentence like 'Can I have a coffee?' can be compressed, but you can't do that with the a of may in 'May I have a coffee?'. All interviewees on the programme agreed that there was a tendency towards simplification in English language development, partly because so many people all over the world speak English and weren't taught all the rules native English speakers were taught at school and in the home.
The programme also looked at aspects of grammar whose usage was increasing. One is the progressive form of stative verbs which, we were once told during English grammar lessons, weren't used in the progressive at all eg I'm loving it, How are you spelling that?. There is also something called the 'footballer's perfect', where footballers in particular use the have been/done/come etc tense when traditionally the simple past was/did/came would have been used (eg He's come down the field and put the ball in the back of the net).
The use of some modal verbs eg could, might imparts a tentative or vague touch to a text. That's why such forms are frequently used in advertising or tabloid headlines eg ... could help you lose weight, ... could be at risk. They can sometimes be very useful verb forms. I came across one example in Christopher Clarke's book about the run-up to the First World War entitled The Sleepwalkers that I have just finished reading. In July 1914 Austria gave Serbia a very tough ultimatum. In Chapter 10 Clarke says '[...] the Serbian ministers invested immense effort in polishing their reply to Vienna in order to create the appearance of offering the maximum possible compliance without compromising Serbian sovereignty'. He describes the Serbian reply as 'a masterpiece of diplomatic equivocation'. One way this was achieved was by using a modal. As Clarke writes, 'They agreed officially to condemn all propaganda aimed at the dissolution of the Austro-Hungarian Empire or the annexation of its territories (though they used a modal form of the verb that avoided the implication that there had ever actually been any such propaganda)'. The reply also said that 'they agreed to dissolve the Narodna Odbrana and any other society "that may be directing its efforts against Austria-Hungary"' - using another modal form.