I have a pretty good desoldering tool (Hakko FR-300). I just can't always get all the solder out from around the pin. Maybe my technique is bad. There's always one or two pins that I can't get the solder out from around. When I keep trying, I might end up inflicting a little damage to the board. Clipping the pins, especially for something like a cheap jellybean opamp, seems much safer.
You should never damage the board with the desoldering tool because its tip should never even touch the board!
A heated tip vacuum desoldering tool like your Hakko is effective and safe when used correctly. I always make sure there is a good amount of solder on the pin(s) being desoldered. This may mean adding a little leaded solder. If I know the joint is lead-free, I always add leaded solder (I have no need to maintain the lead-free status of my purely hobby level work). Bring the tip
straight down over the component pin. When it starts to melt, wiggle the tip back and forth (for ICs, transistors, things with rectangular leads) or in a circle (passives with round leads), but keep the tip
just above the pad when doing this. Don't rub the tip against the pad. For 2+layer boards, you will feel a difference when the solder is finally melted all the way to the other side - the pin will wiggle more easily. It
must melt all the way through; Verify visually if needed.
While still wiggling, activate the vacuum, and
keep the vaccum on while pulling the tip back from the pin until it is free. The motion plus the cooling action of the air rushing in should prevent the pin from sticking to the hole plating. Note that the tip is never pressed into the board. That not only damages the delicate pads, but it actually transfers
too much heat directly to the board, so that the solder remnants in the hole may remain molten for too long, causing the pin to stick to the hole plating. When you perfect this, you will have 40 pin DIPs falling off the board on the first pass.
To help avoid too much heat on the component/board, do every third pin. Then go back and do a second pass, and then a final pass to get them all. This spreads the heat load. If the pin isn't freed and you need to rework it, always re-solder; you need a continuous blob of solder from bottom to top. To avoid overheating, wait little while (desolder a few other pins) then go back, re-solder that pin, wait a while again, then finally go back and desolder.
That's how I do it, and it works great for me, but I'm not an expert and I'm always open to suggestions. The detail of keeping the vacuum on while removing the desoldering tip from the board was an "Aha!" moment for me. I forget where I learned that, but I'm sure it was on this forum. Hopefully this helps you or others.