I think a lot of fans don't realize how impressive the front office of the early Senators was. As you say, they were given nothing in the expansion draft. And only missed the playoffs 4 times before qualifying in 97, kicking off what was at times a dominant 11-year stretch as a contender.
And they did it without drafting any elite players with their early picks, with the exception of Yashin:
1992 - Yashin 2nd overall
1993 - Daigle 1st overall
1994 - Bonk 3rd overall
1995 - Berard 1st overall
1996 - Phillips 1st overall
I have a lot of respect for how well the early franchise was run and for what they accomplished.