Some people will. However most people are enough more social that they will attempt a conversation. If you only put two people together than silence will happen. However if you can get 4 new people at a table odds are at least 2 will start a conversation and the rest will join at least a little.
I used to go to such 4 random people paired up for a meal, then a different 4 next month. (back before work form home my office had a system to match people like that - even though it was a work sponsored program we almost never talked about work even when there was senior management at the table). Even though I'm the silent type there was always a conversation that I ended up joining in. Sure it was work for me to join the conversation, but it was still worth it.
Adding more people often results in more socially awkward, bullying, peer pressure, etc... type situations. Women often put pressure on each other, as to who they "should date" and so unrealistic expectations and hypergamy takes hold, where only the top 20% of men are "good" enough. Even if those women are of "lower ranking" and can't hold on to top ranking men (for more than a night or as a booty call).
Often getting men and women alone together, but in a public setting (so the women feel safe), and putting a time limit on it can work better. Give them an hour, and see if there are any sparks. If not, let them go there separate ways, to find others they can talk to. In that way, there is no obvious peer pressure being exerted on who they "should" choose, it's a matter of chemistry between them.
I said 4 people, not 20. I know what you are saying, and I think around 4 is about right. Less and you start to think about romance and while that can be good not everyone needs it and destroying a marriage is not the goal. More and it is too easy to tune out.
The wrong two women together (or combination of people) can start the peer pressure, bullying, or hypergamy dynamic. Nobody can accurately predict in advance which combination will be troublesome or force their preferences on others. This is why there is the famous term, cock-blocking. It doesn't always happen, but it appears to happen at a high percentage or too often. You can only remove "group dynamics", when there isn't a group involved.
You also appear to condemn romance, which would make matchmaking or seeing if there is any authentic attraction pointless. The group or leader can decide who should date whom based on their own preferences (which can differ from the woman involved), status, looks, fashion, performances, and or dominance (person taking control of the group). Thus back to peer pressure, bullying, and hypergamy.
The problem with "hooking people up" in that way, is the person chosen (approved of) by the group, may not be who the woman really wants or is naturally attracted to. Often, this "forced" kind of coupling goes nowhere (as lacking romance), or leads to just short time dating (as not really each others type). Many women can go along with what they think the group or leader of it wants, and do what is "expected", but can be quietly dissatisfied or prefer something else.
If it's going to be a random group of people, it might as well be a party, club, or other get together. Which would leave the socially awkward (men or women) at the same disadvantage they always have. At least in a big party, they can kind of "hide in plain sight", encounter new people that approach them, or jump to a new random person when they don't like the conversation or vibe.
Allowing just 2 people to meet in public, where both can leave the setting at any time, often results in couplings based on authentic attraction. Of course, nothing is perfect or guaranteed, and such couplings can fail too. However, it's based on what those 2 adult people wanted and decided to do, versus any group pressure or interference.
I'm not condemning romance. I'm saying don't put that pressure one, let it happen.
I agree that sometimes you will get a bad mix, but that won't happen every time.
The idea is every month you have a different group of 4 you meet with for an hour. Small enough that the "wall flowers" cannot hide, often enough that they get pressure to contribute to the conversation. Often enough that the socially awkward will get some practice, but not so often that they get overwhelmed and quit. Low pressure to find someone to marry (include some married people in the groups), but still meeting enough people that there is a chance to find someone in a couple years.
Nothing is perfect, but given South Korea's goals I think it can help. (south Korea has other problems not touched on of course)
I used to go to such 4 random people paired up for a meal, then a different 4 next month. (back before work form home my office had a system to match people like that - even though it was a work sponsored program we almost never talked about work even when there was senior management at the table). Even though I'm the silent type there was always a conversation that I ended up joining in. Sure it was work for me to join the conversation, but it was still worth it.