Do I need a serious reason to enter a US Embassy as a US Citizen?

@Doc provided a very good overall answer. I'll add my own experience in the US embassy in London, UK. I have entered the US embassy a number of times as a US citizen for non-emergency situations and I did have to make appointments every time, stating the intended purpose. Security is high, however it felt that it's not as bad as is sometimes implied. For example, last time I visited about mid-2018, I could get my mobile phone inside and my laptop - no problem. Yes, they x-rayed my bag and I had to go through the metal detector, but the overall experience seemed less thorough than in an airport. Interestingly, once inside, I was directed to the lift and told to go to floor X for whatever my purpose was. Nothing and nobody was there to prevent me from going to any other floor. Probably, if I just started wondering around, I would be asked what I was doing there.

Anecdotally, from a friend of mine who spent some time in some rather dangerous countries in Africa and Middle East (Afganistan, Sudan and a few others), he was telling that in most cases simply showing an American passport would get you inside the embassy straight away. After that they'd ask you the purpose and so on. He did indicate that in some of the smaller African countries the Embassy staff was more than happy to entertain him as a guest due to lack of any other contact with fellow Americans other than the embassy staff themselves.

This was in 1991, but the U.S. Embassy in Sri Lanka encouraged American ex-pats to go there and register with them. So that's technically, "a serious reason", but it also seems like a reasonable excuse for just visiting.

Security at the US Embassy in Tokyo is pretty buff. You must have an appointment to visit. You have to make the appointment online. You can only take a single cellphone, and no other electronics (no, not even a tablet, and not even in substitution for a phone), and no large bags.

https://jp.usembassy.gov/embassy-consulates/tokyo/

If you are going to the Embassy, Japanese police surrounding the place will be very helpful directing you toward the security screening. If you are not going to the Embassy, they will be very helpful with getting you on your way somewhere else.

If you are really curious, you can schedule an appointment for anything. For example, you want to ask an official if some of your papers are valid or not.

For example, saying that your passport was hurted and you want to ask them if it is still valid.

Probably they will check it, read it, and examine if some biomarker readers are still okay in it. After that, you will leave.

Meanwhile, you also get what you wanted. :-)

(P.s. the US embassy is living from your tax, so doing it once is not an ethical breach. Their hard rules are in the fear of some terrorist attacks and not against their own citizens)

Mind what the embassy is: The embassy is your govenment's office of representative to the other countries government. The, historic, primary job of the ambassador is to serve communication between the governments and telling about the mood. That mood extended to intelligence. Also often embassies do serve cultural relationships or similar.

Especially the part about gathering intelligence obviously isn't public. Around the cultural side there sometimes might be events.

Aside from that are consulates. They are often integrated with an embassy and aimed at general public. Like granting visas and renewing passports. Visiting that is simpler. But as boring as any government office.

To offer some information about other embassies, in my case as an Spaniard National I have visited embassies of Spain in other countries just to meet the personnel.

In countries where the diplomatic mission is very small and the national community they represent is small, the embassy personnel is very open and welcome meeting new visitors.

Particularly, the ones I visited had the consulate section and the embassy within the same building. I could freely step into the consulate part not the embassy part.