I have one use case where due to the low volume of emails sent monthly the SAP was configured with Shared IP and not Dedicated IP. SAP subdomain is mc.domain.com for example. The client wants to send emails from the top-level domain, domain.com so we need to subscribe one Private Domain to accomplish this. The issue is that client does not want to add the Shared IP to their SPF list due to the fact is shared among other companies. Will deliverability be impacted due to this or is DKIM and DMARC features the most important ones to ensure good deliverability rates?
Generally, you should only send your emails from an "authenticated domain". It is very unusual to have a top level domain used for sendouts. It is generally advised to have a dedicated subdomain for your email marketing.
"Authenticating" a subdomain via an SAP includes setting the SPF-Record and DKIM. I understand you are not planning to use an SAP, but to use a different domain.
"Private domain" refers to a Salesforce Product, and is referred to as such in the following.
Knowingly not following standard email marketing practices is something I would disencourage.
Details about a private domain in Salesforce Terminology:
A private domain is used as an authentication tool. A Private Domain that is purchased separately for sending is an authenticated domain for use in the FROM address only. It is set up either via a User or Sender Profile, and this type of Private Domain DOES NOT include link or image-wrapping. It has an MX record, SPF/Sender ID and DKIM/Domain Keys.
So your private domain (purchased via Salesforce) would have SPF and DKIM. Typically, such a domain needs be delegated in order for the configuration by Salesforce.
As I understand, you do not want to do that either, but use and reconfigure an already owned domain. And this is where the problems start: Sending from the top level domain also is not something that I would recommend, and you are starting to see why. The domain's administration has to start making changes that are not necessarily beneficial and can have unwanted effects or create conflicts, which explains the (plausible) unwillingness to list a Shared IP in SPF.
Not having SPF configured definitely would have some negative effect. You could potentially test such a setup by sending an email from such a configuration to an inbox on https://www.mail-tester.com/ to get an "exact" measure of how bad that is, but SPF is an industry standard and no provider could really be blamed for blocking your emails, as long as you don't follow it.
There are other repercussions from using the top level domains, e.g.: There is the potential of your sendouts and the "normal" emails coming from that domain (normal day to day business emails) becoming indistinguishable for a recipient server. They will confounding each other, meaning that if someone decides to block your marketing emails, "normal business emails" will also be blocked. In a a B2B scenario, this can be quite severe.
In sum - reconsider. I would personally not recommend to follow this approach through.