I'm not actually sure I buy that, and the volume of bills that are introduced every year is part of the issue. This year, there were 87 days (including weekends) in this year's assembly session.
There were 90 days, as there are every year.
If we round down and say that there were 3,000 bills, that leaves 34 (rounded down) bills to read per day of the session. So if each legislator did literally nothing else than read bills for 8 hours a day, that means they could spend a total of about 15 minutes per bill. Now, most of these people do have an assistant (I know my rep has exactly one staffer, for instance) so if you divide that in half then they get a total of a half hour per bill, and again, that's literally reading bills for 8 straight hours a day for 87 days.
Most if not all Delegates concentrate on the bills before them in committee;
In the House, there were 1832 bills, if they were equally distributed among the 7 committees, that would be 262 (261.7) bills per committee.
In the Senate, there were 1269 bills, equally distributed there would be 181 bills per committee.
Given that they have 69 days to hear the bills and get them over to the other chamber, that works out to 4 bills per day for Delegates and 3 bills per day for Senators.
Then they concentrate on those bills that come out committee as favorable in that 69 days, so let's add 2 more per day for grins and giggles. If they cross over then the process starts all over again with bills in committee and then bills that need voted on, on the floor.
Of course that's not practicably possible - they have to do things like have meetings and hold actual votes, and eat, so I don't think they're being untruthful when they say "we just get too many bills to read them all."
As a former staff member to a Delegate, I call BS, based on how it broken down described above, my Delegate had plenty of time to actually read the bills that came across his desk for his direct attention. In some cases, the staff (paid and volunteers) already had a head start on some of the bills in other committees for floor votes.
I do think it's a problem, though, and personally, I would lean toward the idea that there should be limits on the number of pieces of legislation that any one legislator can introduce during a given session. If you were given one bill a year there would be a LOT less ********.