I would put Teague in that category. The only other 10+ year vets we've had in the Stevens-Ainge era either played actual minutes (Horford, Amir Johnson, Gerald Wallace, David Lee sort of) or were shipped out quickly (Bogans, Jameer, Prince, David Lee sort of). There's definitely some leadership from established vets that you won't find elsewhere, but I don't think there's any sort of cliff where <10 year vets can't provide it. Guys like Gerald Green, Enes Kanter, and Jabari Parker have provided/can provide it, too.
Obviously having people that can really contribute as your 11-15th men would be ideal, but you'll have a hard time finding guys that are both good enough to play real minutes and willing to take a role where they won't normally get any. May as well have a mix of young guys that could contribute at some point and vets that can spend the time mentoring them (especially if those guys have 1 good skill so they can fill a small role if needed)