Re: Is this progress?
"Is there a law which says they must pay out £££millions in share dividends every years "
In effect, yes. The directors of a public limited company have a duty in law to act in the interests of the shareholders (who are, after all the owners). They are also ultimately answerable to the shareholders who own the business via the AGM. That means any investment has to be assessed to be commercially viable. That is produce a return for the shareholders. At some point in
The idea that a company the size of BT can be treated as a startup (overall), is simply ludicrous. The OR side is not, by regulatory action, a "growth business". It's got a turnover of about £5bn, of which about half is line rental, perhaps 10% is GEA-FTTC (or VDSL2) and the rest is mostly private circuits. The line rental price is heavily regulated (and reducing) and the GEA-FTTC product is currently up for review to impose regulatory pricing. Private circuits are heavily price regulated too. There is also likely to be the imposition of a heavily regulated "dark" fibre product in certain areas plus another heavily regulated passive infrastructure (poles & ducts) product. So that core network that you suggest BT pours money into is heavily regulated, has very little room for revenue growth. Current capex is around £1.2bn, and it's very difficult to make a commercial case for vast increases in that amount.
The rest of BT is rather less heavily regulated (which is why you see BT Consumer growing and money being put into that (Sports Rights, bundles and so on). It's also partly why the purchase of EE has gone ahead, a much less heavily regulated industry where there is more prospect of a return for major capital expenditure. There may be smaller parts of the business that also merit higher investment if growth prospects are good, but that's not going to change the big picture.
Finally, shareholders buy into companies for two main reasons. One is yield. Solid, mature blue-chip utilities are expected to produce a yield (the directors get sacked if they don't). Where do you think the likes of investment trusts and pensions get their income? They rely on the likes of BT for that (and used to rely on oil companies and banks too). It's reduction in returns and yields which is partly responsible for pension deficits which hit private and public schemes together (or at least the funded ones).
The second reason is capital growth. A mature company simply can't grow at the rate of a start-up. That's simply because when it has a very large share of a market there isn't the room to grow. Some grow by take-over (witness BT taking over EE), but as that dilutes shareholdings and/or involves more borrowing it dilutes returns unless there are significant synergies (like mutual cost reductions).
So this simplistic quoting of "investment" without consideration for return is never going to work. If shareholders simply see money disappearing into capital investment and their dividend being cut without seeing a chance of getting a return they will simply stop it happening.