1) those that do not use flanking for the stated reasons (added complexity appears to be the most common in the few answers up to now), have you tried playing with it? Or has a decision been taken on the perceived consequence of the rule?
I have not, nor played in a game with it. My earlier comment referred to the Flanking Chain, which was common enough in previous editions, and there is no reason to believe that 5E would be better in this regard (actually, as you point out with 2, it would make it worse).
2) those that do use flanking: it seems to me that in 4E, flanking had a lesser scope for the following reasons:
- a creature could not move around an enemy it was engaged with without provoking an OA, consequently getting into a flanking position was more difficult
- flanking granted a +2 bonus, which is muss less than the advantage it now grants
You are also forgetting Bounded Accuracy. A +2 Bonus in 4E wasn't always significant, but with much lower AC, Advantage is even bigger than you might think. With 5E's movement (which I like, btw), a character should be able to get into flanking position against most enemies, unless the battlefield is constrained (passageways or enemies in formation). So you can get it easier, for a bigger bonus... not my cup of tea.
So do you find that flanking happens very often, and/or becomes an important decider for battles? I.e. is advantage very frequent due to flanking? Do you then perceive it as the norm, as opposed to the exception that it is under the default rules?
Flanking is correctly an optional rule. There is nothing wrong with using it, but it changes several default aspects of the game. Several abilities that grant Advantage are suddenly less powerful, and anything that can cause Disadvantage is that much better (to negate the Advantage).
Also, does using tougher solo or a low-number (2-3) of creatures require these creatures to be stronger to make up for the flanking?
As in a real battle, numbers matter a LOT in 5E. A "solo" monster is already at a significant disadvantage (even with Legendary Actions). Flanking will expand the numbers difference significantly. Conversely, a swarm of weaker creatures (say 4 CR less than the Party Level) become very lethal due to the ability to hit regularly.
Do rogues benefit from a very significant boost with this rule?
Melee Rogues would, which is probably the only reasonable reason to add it. Personally, I'd rather it be a Rogue Ability, rather than a rule for everyone.
I am discussing with my players about introducing flanking. However the fighter in our group is a shield bearer and has a feat that allows him to push an opponent to the ground, and further attacks against the prone enemy are then made with advantage. It seems to me that if advantage can be had more easily, this fighter's feat choice would become less interesting.
Correct. Also, they don't want to shove either, since it will likely take the monster out of Flanking position. Like many optional rules (and houserules) this is better decided at the start of a campaign.
What about using a +2 attack bonus instead of advantage?
If you want to add Flanking, is is probably better. It doesn't discourage Advantage gaining mechanics and doesn't give the rogue free reign. You'll still need to use more creatures, rather than Solo and Elite monsters, because the +2 should still make for a significant increase in damage.