Usually depends on who controls that remotely accessible shared computer. If it is under my control, or under the control of somebody I personally trust, then yes. If it is under the control of somebody else, then no.

Partly, that is because I've been coming to the conclusion that the privacy promises of a company are rather meaningless. In the case of bankruptcy, collected data is treated as an asset, rather than as a liability to be disposed of properly. In the case of acquisition, the database gets transferred to a parent company. For example, with Google buying Fitbit, they will have have access to all data collected by Fitbit. Though (as of yesterday), Google is stating that they don't intend to use this for advertising, I don't trust that not to be "accidentally" merged with google tracking ids in the future.

Indeed, I do not mean to suggest that shared computing is necessarily a net negative. Sharing a remotely accessible computer among trusted friends/family has always been an interesting idea to me because it would allow such easy communication. The way I see it, this is the core idea that underlies "e-mail" on UNIX. A group of people sharing accounts on a computer. UNIX allows easy messaging between accounts. Another group doing the same thing on another computer. Connect the two computers over a telephone line and now we have messaging to people in another group. Today, if you and I can both connect to the same computer, where we both have accounts, that is still an easy way to do messaging, in my opinion. Computers are no longer prohibitively expensive. There is no requirement that the computer belong to a third party. The ongoing problem however is that there needs to be someone who can administer the computer. It is not easy enough for anyone to do. It seems the "sysadmin" is still needed as much today as in the past.