I had to look up the word eschew in my unabridged dictionary so I could get an educated handle on this thread.
Is there a way to prevent users from entering information into cells that have formulas short of protecting the cells.
Now take a close look at what you are asking. You are asking for formulas to not be overriden with unwanted constant entries, or even other formulas.
You did not say you want to guard against drag and drop, or copy and paste, or fill with the fill handle, or hitting the Delete key, or whatever other way there is to obliterate formulas in cells when you are, yes I'll say it, eschewing the native Lock and Protection scheme.
Instead of VBA, the demerits of which have been heretofore delineated, you have one other option, that being data validation.
From any cell on your worksheet press Ctrl+A+A.
From the worksheet menu, click Edit > GoTo > Special and then select Formulas and click OK.
From the worksheet menu, click Data > Validation. In the Allow box select Custom.
In the Formula field enter
=""
That is, type in the equals sign and two double-quote characters.
Set whatever other options you want to on the other 2 DV dialog tabs, and click OK.
Click any cell to deselect all formula-containing cells.
Now when you attempt to enter anything in a formula-containing cell, you will be disallowed by Data Validation.
As I said earlier, there are still a myriad of ways that the formulas are still exposed to for obliteration, but if you have your heart set on no Lock and Protection, so go the risks of eventual disappointing outcome.