The modal verbs of English are a small class of auxiliary verbs used
mostly to express modality (properties such as possibility,
We'll leave aside the main verb 'will' (I was willing him to leave , etc). The unmarked, unstressed use of 'will' to form future constructions (Life on the island seems idyllic. But in two days' time, Krakatoa will erupt catastrophically) does not express modality, but is often taken to be a modal usage because of the syntax involved.
AHD plays safe and just uses the hypernymic term 'auxiliary (verb)' here:
would aux.v. Past tense of will2
- Used to express desire or intent: She said she would meet us at the corner.
- Used to express a wish: Would that we had gone with you!
- Used after a statement of desire, request, or advice: I wish you would stay.
- Used to make a polite request: Would you go with me?
- Used in the main clause of a conditional statement to express a possibility or likelihood: If I had enough money, I would buy a car.
We would have gone to the beach, had the weather been good. See Usage
Note at if.
- Used to express presumption or expectation: That would be Steve at the door.
- Used to indicate uncertainty: He would seem to be getting better.
- Used to express repeated or habitual action in the past: Every morning we would walk in the garden.
(How sensible to give 'how-the-word-is-used' rather than synonynous definitions here.)
Sense '8' is the relevant one. Using 'would' gives the repeated / habitual sense that the past tense doesn't (though the 'always' in OP's example also does this).
When they first met, they would always have picnics on the beach. [repetition]