First time to Spain. Is this too aggressive of an internary?

Well, I'll throw it back to you. Have you traveled this way before? Do you like traveling this way? I know some solo travelers like to do this kind of whistle stop tour, but I would not.
Do note you have to transit through Madrid to go to Toledo.
Where are you flying in and out? I would suggest two places for a week. Fly into Madrid, train to Sevilla, X days, back to Madrid for remainder.

I like to travel fairly quickly, but this would be too quick for me.

Note that you can see Toledo as a day trip from Madrid. Although, I'm sure, it's nicer to spend the night, don't forget that check-out and check-in times usually have a 5-6 hour gap between them, so it might be more convenient to base in Madrid and not do as much changing lodgings. I would also choose either Seville or Barcelona, rather than trying to do both. We took a high-speed train from Madrid to Barcelona. Not sure if a similar option exists for Seville.

4 cities in 7 days? Yes too much. Do Toledo as a day trip from Madrid. Everyone on this site will tell you they love Seville, but I wasn't that impressed. I preferred the Alhambra in Granada.

Choose either Barcelona and Madrid, or Madrid and Seville. It’s a blurred blitz otherwise.

I would drop Barcelona. You can make a day trip to Toledo by train and 2 days in Seville. Please note that it is +/- 3 hours by train between Seville and Madrid. I would look at it as 3 days in Madrid, 1 day in Toledo (including travel), 2 days in Seville and 1 day for travel (both ways) between Madrid and Seville.

If you aren't all-in on Madrid's art museums (which are great), I'd suggest more time in Seville (or Barcelona if you head north instead) than in Madrid.

Spain is a large country; you can't begin to see the highlights in 7 days. No one has pointed out so far that you pass right through Cordoba on the way from Madrid to Seville, but have no time to stop to see even the Mezquita/church.

If you already have your plane tickets, I'd make this a Barcelona/Madrid trip with possibly an in-transit stop in Zaragoza. Zaragoza is a very interesting city, less touristy than Barcelona, and it has a Moorish palace, now turned into a government office building, which you can visit. Alternatively, you could do Barcelona-Madrid with a day-trip to Toledo.

Please don't try to throw Seville into the mix if you're committed to arriving in Barcelona and departing from Madrid. There's lots to see in southern Spain, starting with Seville, Cordoba and Granada. That can be a separate trip.

In short, yes,

No way -for me, at least. As mentioned earlier, it all depends on your travel style. Are you ticking a list or do you really want to soak on what you're seeing?