Why not just use mail-merge software on my computer?

You can do that. But consider:

You need to own the proper software, such as a full install of MS Office.
You need to figure out how to set up mail merge. It's a lot more difficult than using maillists.com.
You can't schedule a mailing time, you must start it manually.
When you hit send, you may discover that your ISP has a limit on how many emails you can send per hour or per day. Your mailing is likely to be interrupted.
You will need to handle unsubscribe requests yourself and diligently keep your spreadsheet(s) current to avoid being labeled a spammer.
Messages you create yourself won't have desirable SPF and DKIM headers which help enhance deliverability.
If you have a list of more than 100 or so contacts, it may take a long time to send all the messages via mail-merge.