Has chess improved that much since Morphy that the odds would not be feasible to give to anyone other than absolute beginners?
This is certainly not the case. Kasparov played a master-level player in 2001 giving move and two pawn odds, and won 2.5-1.5.
In 2008, Larry Kaufman wrote:
...the Elo equivalent of a given handicap degrades as you go down the scale. A knight seems to be worth around a thousand points when the "weak" player is around IM level, but it drops as you go down. For example, I'm about 2400 and I've played tons of knight odds games with students, and I would put the break-even point (for untimed but reasonably quick games) with me at around 1800, so maybe a 600 value at this level. An 1800 can probably give knight odds to a 1400, a 1400 to an 1100, an 1100 to a 900, etc. This is pretty obviously the way it must work, because the weaker the players are, the more likely the weaker one is to blunder a piece or more. When you get down to the level of the average 8 year old player, knight odds is just a slight edge, maybe 50 points or so.
Kaufman also wrote in a 1999 article that a pawn was worth about 200 rating points at master level, and a knight in the opening position was worth about 700, meaning "a FIDE 2115 (USCF 2165) player would be a fair opponent" to Kasparov given knight odds.