It is very common for an advertiser to have a campaign that targets consumers across various channels - DRTV, Email, Display, Search, Billboards etc.
One of the most important thing while measuring from all of these channels is setting up the correct data requirements, tagging etc so that accurate data is available at the desired level to be able to measure the success metrics.
Each channel would also have a different success metric for example in Display, it is very easy to attribute conversion up to the placement level but in case of DRTV, it is very hard. If the campaign involves 5 networks with 2 creatives and running at all day parts - then the number of unique 800 numbers would be very large. Sometimes, it is possible to get them but it can be a challenge even with huge advertisers.
The case explained about DRTV applies to all the offline channels - Billboards, Print media etc
Online is so easy to measure and is as accurate one can get in measuring marketing efforts.
While looking at a holistic picture, it is possible to identify the peaks and valleys based on what media went live at what time. It helps establish the cause and effect relationship across media channels. Sometimes, we see a 1:1 relationship but sometimes it is not worth using a particular channel.
In my opinion, using Email to acquire consumers is not a very good idea, they should be used to maintain a relationship with the consumer. One example could be maintaining a relation with a patient or a car manufacturer could keep sending service updates about the car.