My main concern would be, since the rolls are known ahead of time, behavior might be altered to line up certain checks with certain rolls, in order to get a more desirable result, however unintentional.
Counter example: what if a player made a bunch of rolls ahead of time, recorded them, and just had them on a sheet in front of them. They know their mission is to sneak into guarded area by a market, and convince a noble inside that they're in danger. They see their next rolls on the list are 3, 17, and 18. Given this information, they might be tempted to choose to attempt to fast-talk a merchant on the way out of a piece of fruit, knowing they'll fail and it'll be of little consequence, in order to know they'll have good rolls for their next Stealth and Persuasion checks. A good player would never intentionally do this, but the tempting option is still there, as is the possibility of feeling like they might be accused of doing so if they get particularly lucky.
A way to get around this might be to put the paper in an envelope, and slowly slide it out to reveal the next line as needed. Someone who is really good at memorizing strings of numbers might still be in danger of remembering the pattern, even if you start with the first 1d8 or so ignored to have a random starting point.
One alternative, if you want the ability for players to roll and randomly determine events, but not have enough information to know whether that passed or failed, a modification of #2 might work. Determine a random order of the numbers 1-20, then make a 1-20 table for them on an index card, then consult that when the player rolls. If you're worried about them learning that a 13 on the die is usually a failure and a 5 is usually a success, make multiple cards, flip to the next when used, and periodically shuffle. Actions are still declared and committed to before a check is made, the results are still determined randomly by the player on a fair die roll, but they can't presume how successful it was just on the number before you have a chance to narrate the outcome.