I think it really ends up being about him being the best player. From the games I've seen Nelson is much better at his position than any of the tackles is at OT. For example, McGlinchey is considered by a lot a top 2-3 tackle in this class(and a lot have him no. 1 tackle in the class). You can watch them on the same field next to each other. I don't think there really is a contest about who the better player is... so then the question is - why draft the worse player? The one wild card is Connor Williams, who needs to get back on the field and show he hasn't lost a step after his injury.
BTW I don't think Castonzo is as bad as people make him out to be. He's a good tackle. Right now he's ranked as the 5th best tackle by PFF. PFF is not all perfect and neither is Castonzo but he's not bad. He's allowed 11 pressures in the last 8 games. That's pretty damn good. I wouldn't be rushing to replace Castonzo. There is not any guarantee you are going to get an improvement when you replace him. We have 3 other positions on that line that need MUCH more serious consideration about improvement than LT. IMO, if Brown lasts until the second he would be a phenomenal right tackle. Put Nelson at LG and sign a RG in FA(if you don't think Mewhort is in the future plans) and it is starting to look like hell of a unit.