My example is WindowsCommander, now called TotalCommander. It has just one skippable nag dialog at the start and that’s it. I use it daily, since mid 90s. Since I was just a poor student in poor east European country I didn’t buy it for at least 10 years, not until I started earning decent money. Not the kind of timeline you should make plans for
Now back to question on why you would want to go to freemium. I don’t think typical paying customer installs 2-3 competing products and compare them. Life is too short for that. I assume we’re not talking about something which costs a lot of money. If it costs reasonably for target market, it’s a matter of marketing (to get to customer first), and quality of product during trial to convince customer to purchase it. You should think from perspective of paying customers, you shouldn’t care much if other competitors have much more free users. Yes, bigger market share is a kind of marketing, but users searching for free are not very good customers in the first place.
But this is all theoretical. Maybe we’d have better insight if we knew actual products we’re discussing here.