Yes -- that sounds miserable. Daily is insane. FWIW, at one point in my life I lived in DC (both in the city near Metro Center and later in Arlington near the Courthouse Metro stop). I had a 6 week project in NYC and insisted on flying every week for the miles and in retrospect that was dumb -- especially when my office was right near Penn Station.
The problem with the Shuttle is it sounds easy but once you add everything up it's not so short.
You have to DCA at least 20 minutes before departure (I used to cut it close at DCA but gate closes at T5 so you can't cut it much closer in case security is a problem). There are almost always some sort of weather or traffic related delays so you sit on the tarmac for a while. Once you get to LGA you have to deal with the Uber/Lyft/Taxi situation, then you have to take the 45 - 90 minute drive into the city (depending on where you are going).
Then you have to do the reverse to get back to LGA (and PreCheck can be a big hassle there, you can't cut it as close as with DCA) and if you are doing it daily it's not like you can leave work at 330pm every day to make the 5pm shuttle. So you have to take the last Shuttle -- which is always risky because LGA can be a cluster and so you are always at risk for your evening flight to be cancelled (and if you are on the last one of the day and it's canceled you are hosed).
I would do it on a weekly basis (and get company to pay for hotel) or take the train (but still just do it weekly and get company to pay for a hotel)