Let's go over what teams have drafted a legit starter or signed an undrafted UFA (let's just say homegrown) in the last 15 years and maybe I'll agree with you after breaking it down. Some of this may be skewed by teams that have had a legit starter and their longevity in the league, like the Rangers with Lundqvist, Price with the Canadiens and the Predators with Rinne.
Anaheim - John Gibson this decade. They also found Hiller in the late 00's and Bryzgalov (i think he was their pick?) in the early 00's or late 90's. They're a strong example. Not even factoring in Andersen, who was first drafted by Carolina, before reentering and getting taken a year or two later by Anaheim.
Arizona - Can't remember the last starter they drafted or signed as an undrafted UFA. Might have been in the Winnipeg days. I don't really think Bob Esche counts, as he wasn't a legit starter for long. Usually a platoon guy. They always acquired guys through UFA signing or a waiver pickup like Bryzgalov. Sean Burke, Curtis Joseph, Ilya Bryzgalov, Mike Smith, Antti Raanta, Darcy Kuemper, none of them came from there originally.
Boston - Andrew Raycroft like 20 years ago, who had a ridiculously short shelf life and peak.
Buffalo - Probably Ryan Miller, who was drafted 20 years ago. Enroth wasn't a starter and Ullmark doesn't look like much of one.
Calgary - I can't even remember who they had before Kiprusoff, who didn't come from there, but they've had a bunch of UFA signings like Hiller, Elliott and Smith since then. Rittich is an undrafted UFA, so he's a maybe, but I don't think we can count him as a legit starter just yet.
Carolina - Most people don't realize this, but it was Frederik Andersen, who was originally drafted by them, then re-entered the draft two years later and got picked by Anaheim. Ward in 2002 counts, even though his peak of being good didn't last long.
Chicago - It was actually most recently Antti Niemi as an undrafted UFA signing in 2008 and Crawford before that in the 2003 draft. MAYBE you can count Raanta, who has really only been a starter for one year.
Colorado - Does Peter Budaj from the 2001 draft count? He was a starter there for a couple years. Their most recent guys have both come from Washington.
Columbus - I guess Steve Mason in 2006 or whatever year he was drafted. He was a good starter for one year in Columbus and 2 or 3 others in Philly. Not a long peak though.
Dallas: Marty Turco in 1994. They've usually acquired guys like Belfour, Niemi and Bishop via UFA and Lehtonen via trade.
Detroit: Jimmy Howard in 2003. Mrazek from the 2010 draft for Detroit is a serviceable goalie and had one good season as a legit starter, but I don't see him as a starter. Not even with Carolina right now, do I see him as a legit starter.
Edmonton - It's Dubnyk from 2004.
Florida: Jacob Markstrom is finally looking like a starting goalie. They took him in the 2008 draft.
LA: Jones as an undrafted UFA earlier in the decade. You can also count Bernier in 2006, who was kind of a bust for where he was picked and wasn't a starter for very long. And Quick in 2005. They're probably one of the stronger examples around the league.
Minnesota - Probably Nick Backstrom (the goalie) in 2005 or 2006. I believe he was an undrafted UFA from Europe. Not sure if Harding played enough in any season to really count. They got him in the early 00's. Played really well, but got MS and stopped playing barely into his 30's.
Montreal - Carey Price in 2005.
Nashville - Rinne in 2004. Could be Saros eventually, who was taken earlier in the decade.
New Jersey - Brodeur in 1990.
NYI - Hell if I know? Was it DiPietro in 2000? It was probably DiPietro in 2000. They took guy named Luongo in 1997 too.
NYR - Lundqvist in 2000. They took a couple busts at high picks after that.
Ottawa - Robin Lehner in 2009.
Philadelphia - If it isn't Hart recently then it was probably Hextall in the 80's.
Or Cechmanek in like 2000.
Pittsburgh - Murray about 5-6 years ago.
San Jose - Kiprusoff like 24 years ago.
St. Louis - Probably Ben Bishop in like 2005. It sure isn't Jake Allen and too early to say yet for Binnington.
Tampa - Vasilevskiy in 2012.
Toronto - Tuukka Rask in 2005.
Vancouver - Schneider in 2004.
Vegas - Incomplete. Only been around two years.
Washington - Holtby in 2008. Could be Grubauer a couple years later. They also drafted Varlamov two years before that.
Vegas - Incomplete: Only two years old and not enough time yet.
Winnipeg - Hellebuyck earlier in the decade.
So I guess I'll concede that as far as starters go, the organization hasn't drafted a goalie who became even a decent starting goalie in 24 years. They've done alright with finding NHL caliber goalies, even if just short term backups, but not starters.
A couple other teams that have drafted a starter in the last 15 years (Carolina, Florida, Ottawa, St. Louis, Toronto) had them become starters for other teams and they didn't find success for the teams they were drafted by.
Anaheim, Chicago and Washington have been the most successful in drafting or signing undrafted legit starters in that time. Calgary and Dallas have both failed to do so as well.
Took me parts of 3 hours to do this and at least 3 computer resets.