[GENERAL] Schema design / joins

Hi,
This is more of a general schema design, any advice is much
appreciated.

I have a Organization table. Nearly every other table in the schema
is related to this Org table in some way. So, some tables may be 3 or
4 tables 'away' from the Org table. In order to filter by the org_id,
I need to join a bunch(?3-6) of tables

Simple example below, TeamFees belong to a Team, which belongs to a
Season, which belong to an Org. In order to get all the TeamFees that
belong to a given Org, I need to join all the tables which isn't a big
deal, but I'm just wonder if putting an extra 'org_id' on Team fees
would help anything...

** Is it a bad idea to put an extra FK 'org_id' on the TeamFees table
to avoid all the joins?
** What about putting an 'org_id' on every table? (it seems somewhat
redundant/unnecessary to me)

I've never had any formal education in rdbms, but from what I can
gather, foreign keys are meant to ensure data consistency, not reduce
the number of joins required. Although, it sure seams like it would
simplify the queries if I stuck extra 'org_id' columns in certain
places. I don't have any particular reason that I'm trying to avoid
joins -- I'm just wondering if there is something simpler or if 'thats
just how it is.'

I would really, really appreciate any suggestions from folks with
rdbms schema design experience! Thanks!

__Orgs__
id
name

__Seasons__
id
org_id fk(orgs.id)
name

__Teams__
id
season_id fk(seasons.id)
name

__TeamFees__
id
team_id fk(teams.id)
*org_id <--- (?put extra fk here to avoid many joins?)