Thank you for your suggestion. I too have been touched by the loneliness of people I've met in nursing homes over the years, and I've seen how grateful they are when someone visits them, or even just says hello to them.
Some churches do have programs to reach out to those who are in nursing homes or other facilities where people may not have many visitors. Many nursing homes also have regular chapel services, often led by a local pastor. The Bible says, "Religion that God our Father accepts as pure and faultless is this: to look after orphans and widows in their distress" (James 1:27).
But I'm sure much more could be done–particularly as our population ages and more and more people find themselves in such places. If your church is not already involved in this kind of ministry I'd encourage you to talk with your pastor about it, and suggest that someone from your church contact the nursing homes in your area to see what can be done to help them.
At the same time, if God has given you a special concern for those who are older, make time in your schedule to visit some of them. Listen to them ... encourage them ... pray with them ... read the Bible to them. Soon many of them will die and enter eternity, but God can use you to point them to Christ, who alone is "able to save completely those who come to God through him" (Hebrews 7:25).