Missed a connection due to delayed baggage

You can try. Sometimes you are successful.

According to the relevant EU-regulation you may have a right to compensation, EUR600 in your case, unless

The Airline is not obliged to provide cash compensation in the case of extraordinary circumstances which could not have been foreseen even if the airline took all reasonable precautions, according to Article 5, Paragraph 3.

In practice I recommend the following approach:

1. If the delay clearly was due to unforeseen circumstances (e.g. weather, but also strikes in most cases), give it up here or go directly to step 3
2. Contact the airline, make your claim according to the regulation and set them a deadline, at least 2 weeks would be usual but also more
3. If they do not respond or respond negatively, a convenient way is to sell your claim to a lawyer specialized in this for a commission (e.g. this one comes up first on google, they take 25% of the compensation). I believe those companies only take up cases that they deem successful in the first place.
4. Alternatively in Germany there is a "Schlichtungsstelle" which offers a mediation process free of charge after you went through step 2. I can't find confirmation of this, but a link to Germany might be needed (e.g. flight departed from Germany), for sure the company needs to be a member on this list. You can still proceed to step 3 or 5 if you are not happy with their suggestion or the airline does not accept it.
5. Get a lawyer do fight for your claim, up to in court. You should be really sure you are right though and aware of the legal costs involved.

The success of these claims depends on individual circumstances both of your delay and how well you fare in the legal process and I think it is very difficult to give individual advice. You can try, but don't get fixated on it and e.g. step 5 should really be an exception.
Airlines of course notoriously tend to dismiss claims so don't give up too early. Lufthansa once claimed a delay was due to a weather delay of the aircraft on a previous flight, whereas the pilot had announced during the flight that crew had been stuck in traffic on the way to the airport. I was successful in getting compensation only after going through steps 2 and 4.

The EU recently published clarification regarding various EU262/2004 issues that were previously unclear. In your case the text of interest is:

In accordance with Article 3(1)(a), passengers who missed a connection within the EU, or outside the EU with a flight coming from an airport situated in the territory of a Member State, should be entitled to compensation, if they arrived at final destination with a delay of more than three hours. Whether the carrier operating the connecting flights is an EU carrier or a non-EU carrier is not relevant.

For what it's worth, I obtained compensation a year or two ago in a similar situation. I flew EU to US and arrived with a 2 hour delay, missing an internal connection in the US. I was given hotel and food vouchers, rebooked for the next day and received 600 Euro compensation from BA without them raising any objection. In my case the cause of the delay was clearly the fault of the airline.

Given that you did fly to your destination, a refund is unlikely. You can still complain and they may offer you a voucher for a future flight (or part thereof). It is at the discretion of the airline and may depend on your status with them.

As for the circumstances, they seem to have performed well in terms of service, given that the delay could easily have been beyond their control. Not all airports in the US need you to transfer luggage and it may be good to learn which ones do an do not for when you compare future trips. I often have a US stop coming from South America and I know that Miami Airport requires the manual luggage transfer but not Atlanta (at least with Delta or AA).