Actually, most shuls daven too quickly. The problem lies with the davening, not the talking. Here’s my take.
Most of us had zero formal education, or even role modeling that taught us to properly oriented to tefiloh. Boys’ yeshivos rarely, if ever, have classes on tefiloh. Some girls’ schools do, but the talking problem we are addressing is on the men’s side of the mechitzah. What we do have is a proclamation of “don’ts”. The huge published signs about the issur to talk during davening and laining, the custom signs in some shuls about how talking from beginning to end of davening is not tolerated, the drashos about this, the police who patrol the shul to admonish those that talk, and the literature and videos from various rabbonim on the subject are all versions of “don’t”. There seems to be some impact, but the discussion here implies that the impact is minimal.
I propose something that was alluded to in several prior comments here. Instead of rebuking talkers, instead of highlighting the don’ts (I am keenly aware of the halacha that tells us גוערים בו), instead of hanging signs or policing, I note that the worst aveiroh is not the talking part but the “not davening” part. If we could encourage a proper attitude toward tefiloh, if we could educate everyone on how precious it is to be able to talk to Hashem directly, being invited into His Home three times a day, if we could understand what we ask, if we could appreciate that our praises to Him are benefitting us, etc., the problem is solved. People should socialize, and there is ample time before and after davening to accomplish that. To waste the opportunity to speak to Hashem is a terrible loss, and that direction of education (by example plus teaching) would likely make a massive change.