The real question that would need to be asked is “does the 40% who use landlines still compriae a reasonable cross section of society. If it does then that’s probably enough people from which to get a sample. If not....they better find some new method. Or they can resort to just making up the numbers out of whole cloth the way the government does with number of immigrants, unemployment etc....
The anecdotal evidence is that people with landlines tend to skew older, whiter, more conservative, and more rural. That’s what I have heard. Disproportionate numbers of millenial “yuppies” only have a cellular phone.
The percentage of people that have landlines is not the problem as the pollsters can weigh certain demographics more heavily. The problem with that is that when the pollster finally does reach the 28 year old single white male with a landline making 75k a year, his answers may be outliers for his cohort. His answers end up having too much weight.