Replacing a bathroom faucet is a fairly straight-forward service. One thing to note however is the time involved based on your particular sink/cabinet configuration. The fastest job would be in a box vanity with a one-piece integrated taps and spigot. The slowest job is a pedestal sink with a 3 piece tap, spigot, tap set-up. Of course a new drain that comes with the faucet will add additional time, unless you opt to keep the old one.
When it comes to drains, most will opt to have the new included drain installed, so that the finish on the faucet and drain match. A new brushed nickel faucet isn’t going to look quite right with an old chrome drain. Here’s the problem – most new faucets (MOEN for example) include a plastic drain assembly. Because it is plastic, the lip is necessarily thicker for strength. Not only is it thicker, it has integrated ribs. There is a lot of torque on the drain nut, and making a plastic drain thinner would likely cause it to snap. The result is that the new drain is going to sit higher on the bottom of your sink, and water will not drain completely.
Is there any solution ?
If a small amount of standing water is something you don’t think you can get used to, then a metal drain is the answer – they are still probably as thin as your present (old) drain.
Visit the store with your new faucet, and purchase a matching finish metal drain. I imagine manufacturers include a plastic drain to keep cost as low as possible. A new metal drain is going to cost about 30-40 dollars if you can find the right match in a big box store, and maybe a lot more if you require a custom finish. I would check with the manufacturer directly to see if they can provide, or suggest where to get a custom finish drain to match your new faucet.
I’ve come across this situation a lot, and unfortunately between faucet jobs I forget the issue, and don’t give a heads up to the customer. My apology if I’ve not pointed this out to you before replacing a drain in the past. So going forward I will make sure to include this article with inquiries for faucet replacement.