Tradition. To quote from "Some Traditions and Customs of the House" 1
The style of debate in the House has traditionally been one of cut-and-thrust; listening to other Members' speeches and intervening in them in spontaneous reaction to opponents' views. It is thus very different from the debating style in use in some overseas legislatures, where reading of set-piece speeches from a podium or from individual desks is more common.
It also states that:
To maintain the spontaneity of debate, reading a prepared speech is not allowed though the use of notes is.
So, a debate in a hypothetical legislative chamber could involve each delegate who wants to participate standing up, reading out a speech from a script, and then sitting down.
But the longstanding tradition in the Commons is that a debate involves a lot of back-and-forth. Giving way when other MPs wish to intervene is one way in which this is achieved.
To address other points in the question:
Is the reason for giving way merely about being seen to be a good parliamentary citizen, thereby earning soft favour with other MPs, the Speaker(s), and - possibly - their constituents?
Well, I'm speculating a little, but one can imagine that if an MP gains a reputation for frequently taking interventions, then other MPs may be more willing to take interventions from that MP, and the Speaker may look favourably on the MP as someone who is, as you say, "a good parliamentary citizen".
If MP1 has the floor, and MP2 and MP3 indicate to them that they wish to intervene, the choice of whether to give way - and who to give way to - is entirely in the gift of MP1, and is never required. If time is limited, or MP1 wants to make more progress on what they were planning to say, then they are free to decline. If MP1 accepts an intervention from, say, MP2, the Speaker is not involved, other than to confirm the choice of MP2 by calling their name (often after they've started talking) - and of course to maintain order.
To give one such example (Hansard, 29 Jan 2019):
Angela Smith: rose—
Jeremy Corbyn: I am making progress, Mr Speaker. [Interruption.]
Mr Speaker: Order. Is the right hon. Gentleman giving way?
Jeremy Corbyn: indicated dissent.
Mr Speaker: He is not giving way. [...] The rules of this House are clear. If the Leader of the Opposition wishes to give way, he does so; if he does not wish to do so, he does not have to do so.
To return to the question:
Or is there some potential tactical advantage that might be gained by giving way, raising the probability of swaying a debate in the MP’s favour?
If an intervention is met with a good response or counterargument, then maybe. It's a bit of a gamble.
Note that interventions are also used to ask for clarification, or to encourage the MP to elaborate on the point they've just made. This kind of intervention is commonly used when a minister is making a statement to the House. (Once the minister has completed their statement, the Speaker will then call MPs to ask questions in the normal way, just like in a debate.)
(1) House of Commons Information Office, Factsheet G7.