Does it make sense to build a product similar to a recently acquired one?

I was one of the early, and daily, users of a small web app developed four years ago. Exactly one year ago, the app was acquired by a bigger company and shut down. It became now part of the services offered by the bigger company, if you want to use the service, you have to be a paying member of the bigger brand. I was thinking, why don't I go ahead and build something similar. I'm a software engineer and 1) will enjoy my time building the tool 2) others might pay for it 3) kind of long term, but if it's good enough it might be acquired as well. I'm not sure though if it makes any sense to build something that already existed before and was acquired by a big player. Curious to know what you think and if I should disregard the idea and focus on something…