Very weak? If anything he received a buff like everybody else. Having no need to pay influence with your religion in their lands is pretty damn powerful stuff.
In absolute terms it's an advantage to gain influence more easily, as anyone can post-G&K; in relative terms Greece fares far worse because they just get so much less out of it than Siam, as well as the Greek benefit simply being inherently less useful to anyone else. And since anyone can be permafriends, and anyone if they so desire can minimise natural influence loss with the same opener and religious belief, not losing natural influence really is trivial. Most of the time you'll lose allies through other civs gaining greater influence than you, through election-rigging, or occasionally through coups. Greece does nothing to defend against any of those - you still need to actively cultivate influence. And if you compare Greece + Patronage + belief with other civ + Patronage + belief, rather than just Greece + Patronage + belief vs. other civ with neither, you'll appreciate just how trivial the Greek UA itself is.
There's also no need to criticize the UA for not helping to increase influence in the first place since G&K has so many CS quests now. If anything that should be a good thing for Greece compared to other civs. Without a plethora of CS quests the Sweden UA would shine a lot more brilliantly.
Spoken, I suspect, like someone who hasn't played Sweden. Even with a plethora of CS quests you won't usually be able to focus resources on allying with more than three or four for most of the game. With Sweden I can retain reliable, uncoupable alliances with over half a dozen, and the more I ally, the more I can keep as they spawn GPs for me.
However with more CS quests Greece can easily net influence and will stay longer in alliance with them without having to spend gold.
When do you ever lose an alliance in G&K through natural influence loss? Practically never past the very earliest game stages - usual influence just from two quests is 80-100, and by the time that runs down you'll have completed more quests or, past Renaissance, be rigging elections regularly. And anyone can (and if they want to make use of CSes likely will) take the Patronage opener - the Greek UA is unnoticeable if you go that route, and of marginal use otherwise. Moreover, this was a thread comparing civs to find the 'best', and that means Greece has to be compared against its competition rather than seen in isolation.
Can Greece maintain influence with CSes? Yes, but far less effectively than Sweden, or than an economic civ that can just buy extra influence. Consider the maths: if you lose 20 influence over 40 turns, and Askia loses 20 influence over 20 turns, all Askia needs to do to break even with Alexander is to make 250 gold more than Alex does in those 40 turns. Which he will easily do at any stage past the very earliest game, and probably then as well - in that time period he saves 80 gold per temple even without camp/city captures. And Songhai fell out of the race early.
Can it give you more of an advantage per CS than other civs? Yes, except for Siam and Sweden - or, as above, any civ with the minor economic boost needed to outcompete Alex.
Can it give you an influence boost high enough to protect your allies from coups? No ... unlike Sweden.
Can you use it for early warmongering? Yes, but much less effectively than Persia or most civs with early ranged UUs, due to a UU that's much less effective at taking cities.
Is it good enough at both warmongering and CS control together to justify its relative weakness in either sphere? Not a chance.
Whether or not you utilize the UU is completely up to you, but successful early conquests IS game-changing.
Of course it is - the point is that the Hoplite isn't particularly suited to it. Most early game conquests revolve around ranged troops and just use the spear to capture the city; the Hoplite's extra strength is insufficient by itself. The main exception - Persia - has a UU that is simply better at doing the job, because it can stand up much better to city defences and can attack a city, retreat to recover quickly, and get back into the fight without the need for archer support.
If Greece's UU help with that, then they will have impact. An early conquest pretty much means more gold, which means more CS bribing. His UU and UA can have some decent synergy, actually.
And if going for that strategy, civs I'd rather have would include:
1. Persia. Much better at gold production; if used for CSes, far outweighs Alex's advantage, and more generally gold is just a more versatile resource than CS influence. Plus the early conquest advantage, particularly during a Golden Age (which can come early enough, potentially).
2. Songhai: +2 strength on a spearman, or triple gold from capturing that city and a consequent boost to CS influence?
3. Sweden: Go on an early attack, conquer the city, get a GG into the bargain - huge amount of early CS influence.
4. Siam: I get more for my influence.
5. The Huns: No CS advantages at all, but capturing the cities is easy and I can then do it again once or twice more and gain yet more cash.
and marginally:
6. Austria: Then you can buy the CS when you're done with its bonuses.
So, in summary, you're selling Greece on its best-scenario strategy, which it is not brilliantly-suited to execute, and there are at least five civs that do it better only two of which made the top 10 (and those didn't make it because they could execute an early conquest + bribe). Greece's best strategy just isn't seen as being good enough to warrant the inclusion of superior competitors, let alone Greece itself.