Agreed, I have proposed this in the past. Especially with all of the travel involved in CL and EL, it just isn't smart.
As you rightly point out, the leagues may need to be stopped sometime next season. Congested calendars will mean a stoppage of a couple weeks will force us into the same situation again next year. The added layer obviously, if CL/EL are happening, is what if say Italy and Spain go on lockdown but other countries do not? It'll just be a mess.
The issue though is, of course, money. UEFA will not want to give up their money. Another factor though is many clubs rely on CL revenue to support their wage bills. If there is no CL next year then a bunch of teams may need to cut wages.
It's going to be a mess no matter what happens. It just shows you how intertwined money and sport are now though. Depressing really.