It depends on the couple. If either party believes that proposing is a man's job, it probably won't work well. The woman may be disappointed in not getting a proposal and a man may say "I will propose when I'm ready and not before". My ex-husband said that when I wanted to know his intentions.
However, if both parties are progressive and believe in equality of the sexes, I see no problem with it.
For what it's worth, I suggested marriage to my partner. I one night I just said "hey, do you think we should get married?" and he said yes. Though after a weekend's discussion we didn't end up getting married because our reasons were wrong. I mainly wanted a name change and he mainly wanted a party with lots of guests and flowers and groomsmen and bridesmaids and the dress and everything (blech). So we got a new bathroom instead. And later on I had my name legally changed to match his and our kids.
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.