Google uses the API key to identify who is sending those requests. Google will impose a quota. As you've correctly identified, if Google receives too many requests using that API key, they'll blacklist the API key. If that happens, your own site/app will stop working.
Therefore, there are risks to leaving the API key in the clear on your page. These risks are somewhat modest: someone who gains the API key doesn't get root on your systems, but they might end up causing your app to stop working.
If this risk bothers you, then don't put the API key on your web page. Instead, have the client issue an AJAX request to your server, and then have the server issue the request to Google and return the results back to the client. This way, the Google API key is never exposed to the client.