Search rankings vary by location, and checking them manually from your own IP gives you a personalized result, not what an average searcher in a target city actually sees.
Why location-specific proxies matter
To check how a page ranks in a specific city or country, you need a proxy physically located there, since search engines localize results based on the requester's apparent location, not just the search query's language.
Avoiding search engine rate limits
Search engines aggressively rate-limit and CAPTCHA automated queries from a single IP. Rank-tracking tools rotate across many proxies specifically to run hundreds of daily keyword checks without one IP taking the full brunt of that detection.
What this means practically
If you're checking rankings for a handful of keywords occasionally, doing it manually is fine. Anything approaching daily automated tracking across many keywords needs a proper rotating proxy setup to stay usable.